Exercise 5A
Question 1:
Write the fraction representing the shaded portion:
(i) Figure
(ii) Figure
(iii) Figure
(iv) Figure
(v) Figure
(vi) Figure
ANSWER:
(i) The shaded portion is 3 parts of the whole figure
∴∴ 3434
(ii) The shaded portion is 1 parts of the whole figure
∴∴ 1414
(iii) The shaded portion is 2 parts of the whole figure.
∴∴ 2323
(iv) The shaded portion is 3 parts of the whole figure.
∴∴310310
(v)The shaded portion is 4 parts of the whole figure.
∴∴4949
(vi) The shaded portion is 3 parts of the whole figure.
∴∴ 3838
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Question 2:
Shade 4949 of the given figure.
Figure
ANSWER:
Page No 82:
Question 3:
In the given figure, if we say that the shaded region is 1414, then identify the error in it.
Figure
ANSWER:
The given rectangle is not divided into four equal parts.
Thus, the shaded region is not equal to 1414 of the whole.
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Question 4:
Write a fraction for each of the following:
(i) three-fourths
(ii) four-sevenths
(iii) two-fifths
(iv) three-tenths
(v) one-eighth
(vi) five-sixths
(vii) eight-ninths
(viii) seven-twelfths
ANSWER:
(i) 3434 (ii) 4747 (iii) 2525 (iv) 310310 (v) 1818
(vi) 5656 (vii)8989 (viii) 712712
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Question 5:
Write down the numerator and the denominator of each of the fractions given below:
(i) 4949
(ii) 611611
(iii) 815815
(iv) 12171217
(v) 5151
ANSWER:
Numerator Denominator
(i) 4 9
(ii) 6 11
(iii) 8 15
(iv) 12 17
(v) 5 1
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Question 6:
Write down the fraction in which
(i) numerator = 3, denominator = 8
(ii) numerator = 5, denominator = 12
(iii) numerator = 7, denominator = 16
(iv) numerator = 8, denominator = 15
ANSWER:
(i)3838 (ii) 512512 (iii)716716 (iv) 815815
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Question 7:
Write down the fractional number for each of the following:
(i) 2323
(ii) 4949
(iii) 2525
(iv) 710710
(v) 1313
(vi) 3434
(vii) 3838
(viii) 914914
(ix) 511511
(x) 615615
ANSWER:
(i) two-thirds
(ii) four−-ninths
(iii) two−-fifths
(iv) seven−-tenths
(v) one−-thirds
(vi) three−-fourths
(vii) three−-eighths
(viii) nine−-fourteenths
(ix) five−-elevenths
(x) six−-fifteenths
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Question 8:
What fraction of an hour is 24 minutes?
ANSWER:
We know: 1 hour = 60 minutes
∴ The required fraction = 2460=252460=25
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Question 9:
How many natural numbers are there from 2 to 10? What fraction of them are prime numbers?
ANSWER:
There are total 9 natural numbers from 2 to 10. They are 2, 3, 4, 5, 6, 7, 8, 9, 10.
Out of these natural numbers, 2, 3, 5, 7 are the prime numbers.
∴ The required fraction = 4949.
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Question 10:
Determine:
(i) 2323 of 15 pens
(ii) 2323 of 27 balls
(iii) 2323 of 36 balloons
ANSWER:
(i) 2323 of 15 pens = (231×1551) = 10 pens231×1551 = 10 pens
(ii) 2323 of 27 balls = (231×2791) = 18 balls231×2791 = 18 balls
(iii) 2323 of 36 balloons = (231×36121) = 24 balloons231×36121 = 24 balloons
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Question 11:
Determine:
(i) 3434 of 16 cups
(ii) 3434 of 28 rackets
(iii) 3434 of 32 books
ANSWER:
(i) 3434 of 16 cups = (341 × 1641) = 12 cups341 × 1641 = 12 cups
(ii) 3434 of 28 rackets = (341 × 2871) = 21 rackets341 × 2871 = 21 rackets
(iii) 3434 of 32 books = (341 × 3281) = 24 books341 × 3281 = 24 books
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Question 12:
Neelam has 25 pencils. She gives 4545 of them to Meena. How many pencils does Meena get? How many pencils are left with Neelam?
ANSWER:
Neelam gives 4545 of 25 pencils to Meena.
(451 × 2551) = 20 Pencils 451 × 2551 = 20 Pencils
Thus, Meena gets 20 pencils.
∴ Number of pencils left with Neelam = 25 −- 20 = 5 pencils
Thus, 5 pencils are left with Neelam.
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Question 13:
Represent each of the following fractions on the number line:
(i) 3838
(ii) 5959
(iii) 4747
(iv) 2525
(v) 1414
ANSWER:
Draw a 0 to 1 on a number line. Label point 1 as A and mark the starting point as 0.
(i) Divide the number line from 0 to 1 into 8 equal parts and take out 3 parts from it to reach point P.
(ii) Divide the number line from 0 to 1 into 9 equal parts and take out 5 parts from it to reach point P
.
(iii) Divide the number line from 0 to 1 into 7 equal parts and take out 4 parts from it to reach point P.
(Iv) Divide the number line from 0 to 1 into 5 equal parts and take out 2 parts from it to reach point P.
(v) Divide the number line from 0 to 1 into 4 equal parts and take out 1 part from it to reach point P.
Page No 85:
Exercise 5B
Question 1:
Which of the following are proper fractions?
12,35,10774, 2, 158,1616,1011,231012,35,10774, 2, 158,1616,1011,2310
ANSWER:
12, 35, 101112, 35, 1011
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Question 2:
Which of the following are improper fractions?
32,56,94,88, 3, 2716,2331,1918,1013,262632,56,94,88, 3, 2716,2331,1918,1013,2626
ANSWER:
A fraction whose numerator is greater than or equal to its denominator is called an improper fraction. Hence, 32, 94, 88, 2716, 1918 and 262632, 94, 88, 2716, 1918 and 2626 are improper fractions.
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Question 3:
Write six improper fractions with denominator 5.
ANSWER:
Clearly, 65, 75, 85, 95, 115and 12565, 75, 85, 95, 115and 125 are improper fractions, each with 5 as the denominator.
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Question 4:
Write six improper fractions with numerator 13.
ANSWER:
Clearly, 132, 133, 134, 135, 136, 137132, 133, 134, 135, 136, 137 are improper fractions, each with 13 as the numerator.
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Question 5:
Convert each of the following into an improper fraction:
(i) 557557
(ii) 938938
(iii) 63106310
(iv) 35113511
(v) 1091410914
(vi) 1271512715
(vii) 88138813
(viii) 51235123
ANSWER:
We have:
(i) 557 = (5 × 7) + 57 = 407557 = (5 × 7) + 57 = 407
(ii) 938 = (9 × 8) + 38 = 758938 = (9 × 8) + 38 = 758
(iii) 6310 = (6 × 10) + 310 = 63106310 = (6 × 10) + 310 = 6310
(iv) 3511 = (3 × 11) + 511 = 38113511 = (3 × 11) + 511 = 3811
(v) 10914 = (10 × 14) + 914 = 1491410914 = (10 × 14) + 914 = 14914
(vi) 12715 = (12 × 15) + 715 = 1871512715 = (12 × 15) + 715 = 18715
(vii) 8813 = (8 × 13) + 813 = 112138813 = (8 × 13) + 813 = 11213
(viii) 5123 = (51 × 3) + 23 = 15535123 = (51 × 3) + 23 = 1553
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Question 6:
Convert each of the following into a mixed fraction:
(i) 175175
(ii) 627627
(iii) 10181018
(iv) 95139513
(v) 81118111
(vi) 87168716
(vii) 1031210312
(viii) 1172011720
ANSWER:
(i) On dividing 17 by 5, we get:
Quotient = 3
Remainder = 2
∴ 175 = 3 +25 = 325 175 = 3 +25 = 325
(ii) On dividing 62 by 7, we get:
Quotient = 8
Remainder = 6
∴ 627 = 8 +67 = 867 627 = 8 +67 = 867
(iii) On dividing 101 by 8, we get:
Quotient = 12
Remainder = 5
∴ 1018 = 12 +58 = 1258 1018 = 12 +58 = 1258
(iv) On dividing 95 by 13, we get:
Quotient = 7
Remainder = 4
∴ 9513 = 7 +413 = 7413 9513 = 7 +413 = 7413
(v) On dividing 81 by 11, we get:
Quotient = 7
Remainder = 4
∴ 8111 = 7 +411 = 7411 8111 = 7 +411 = 7411
(vi) On dividing 87 by 16, we get:
Quotient = 5
Remainder = 7
∴ 8716 = 5 +716 = 5716 8716 = 5 +716 = 5716
(vii) On dividing 103 by 12, we get:
Quotient = 8
Remainder = 7
∴ 10312 = 8 +712 = 8712 10312 = 8 +712 = 8712
(viii) On dividing 117 by 20, we get:
Quotient = 5
Remainder = 17
∴ 11720 = 5 +1720 = 51720 11720 = 5 +1720 = 51720
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Question 7:
Fill up the blanks with ‘>’, ‘<‘ or ‘=’:
(i) 12 112 1
(ii) 34 134 1
(iii) 1 671 67
(iv) 66 166 1
(v) 30163016 130163016 1
(vi) 115 1115 1
ANSWER:
An improper fraction is greater than 1. Hence, it is always greater than a proper fraction, which is less than 1.
(i) 12 < 112 < 1
(ii) 34 < 134 < 1
(iii) 1 > 671 > 67
(iv) 66 = 166 = 1
(v) 30163016 = 130163016 = 1
(vi) 115 > 1115 > 1
Page No 86:
Question 8:
Draw number lines and locate the following points:
(i) 14, 12, 34, 4414, 12, 34, 44
(ii) 18, 28, 38, 58, 7818, 28, 38, 58, 78
(iii) 25, 35, 45, 8525, 35, 45, 85
ANSWER:
(i) Draw a number line. Mark 0 as the starting point and 1 as the ending point.
Then, divide 0 to 1 in four equal parts, where each part is equal to 1/4.
Show the consecutive parts as 1/4, 1/2, 3/4 and at 1 show 4/4 = 1.
(ii) Draw 0 to 1 on a number line. Divide the segment into 8 equal parts, each part corresponds to 1/8. Show the consecutive parts as 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8 and 8/8. Highlight the required ones only.
(iii) Draw 0 to 2 on a number line. Divide the segment between 0 and 1 into 5 equal parts, where each part is equal to 1/5.
Show 2/5, 3/5, 4/5 and 8/5 3 parts away from 1 towards 2. (1 < 8/5 < 2)
Page No 89:
Exercise 5C
Question 1:
Write five fractions equivalent to each of the following:
(i) 2323
(ii) 4545
(iii) 5858
(iv) 710710
(v) 3737
(vi) 611611
(vii) 7979
(viii) 512512
ANSWER:
(i) 23 =2×23×2 = 2×33×3= 2×43×4= 2×53×5 = 2×63×623 =2×23×2 = 2×33×3= 2×43×4= 2×53×5 = 2×63×6
∴ 23 = 46 = 69 = 812 = 1015 = 121823 = 46 = 69 = 812 = 1015 = 1218
Hence, the five fractions equivalent to 2323 are 46, 69, 812, 1015 and 1218 46, 69, 812, 1015 and 1218.
(ii) 45 =4×25×2 = 4×35×3= 4×45×4= 4×55×5 = 4×65×645 =4×25×2 = 4×35×3= 4×45×4= 4×55×5 = 4×65×6
∴ 45 = 810 = 1215 = 1620 = 2025 = 243045 = 810 = 1215 = 1620 = 2025 = 2430
Hence, the five fractions equivalent to 4545 are 810, 1215, 1620, 2025 and 2430 810, 1215, 1620, 2025 and 2430.
(iii) 58 =5×28×2 = 5×38×3= 5×48×4= 5×58×5 = 5×68×658 =5×28×2 = 5×38×3= 5×48×4= 5×58×5 = 5×68×6
∴ 58 = 1016 = 1524 = 2032 = 2540 = 304858 = 1016 = 1524 = 2032 = 2540 = 3048
Hence, the five fractions equivalent to 5858 are 1016, 1524, 2032, 2540 and 3048 1016, 1524, 2032, 2540 and 3048.
(iv) 710 =7×210×2 = 7×310×3= 7×410×4= 7×510×5 = 7×610×6710 =7×210×2 = 7×310×3= 7×410×4= 7×510×5 = 7×610×6
∴ 710 = 1420 = 2130 = 2840 = 3550= 4260710 = 1420 = 2130 = 2840 = 3550= 4260
Hence, the five fractions equivalent to 710710 are 1420, 2130, 2840, 3550 and 4260 1420, 2130, 2840, 3550 and 4260.
(v) 37 =3×27×2 = 3×37×3= 3×47×4= 3×57×5 = 3×67×637 =3×27×2 = 3×37×3= 3×47×4= 3×57×5 = 3×67×6
∴ 37 = 614 = 921 = 1228 = 1535= 184237 = 614 = 921 = 1228 = 1535= 1842
Hence, the five fractions equivalent to 3737 are 614, 921, 1228,1535 and 1842614, 921, 1228,1535 and 1842.
(vi) 611 =6×211×2 = 6×311×3= 6×411×4= 6×511×5 = 6×611×6611 =6×211×2 = 6×311×3= 6×411×4= 6×511×5 = 6×611×6
∴ 611 = 1222 = 1833 = 2444 = 3055= 3666611 = 1222 = 1833 = 2444 = 3055= 3666
Hence, the five fractions equivalent to 611611 are 1222, 1833, 2444, 3055 and 3666 1222, 1833, 2444, 3055 and 3666.
(vii) 79 =7×29×2 = 7×39×3= 7×49×4= 7×59×5 = 7×69×679 =7×29×2 = 7×39×3= 7×49×4= 7×59×5 = 7×69×6
∴ 79 = 1418 = 2127 = 2836 = 3545= 425479 = 1418 = 2127 = 2836 = 3545= 4254
Hence, the five fractions equivalent to 7979 are 1418, 2127, 2836, 3545 and 4254 1418, 2127, 2836, 3545 and 4254.
(viii) 512 =5×212×2 = 5×312×3= 5×412×4= 5×512×5 = 5×612×6512 =5×212×2 = 5×312×3= 5×412×4= 5×512×5 = 5×612×6
∴ 512 = 1024 = 1536 = 2048 = 2560= 3072512 = 1024 = 1536 = 2048 = 2560= 3072
Hence, the five fractions equivalent to 512512 are 1024, 1536, 2048,2560 and 30721024, 1536, 2048,2560 and 3072.
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Question 2:
Which of the following are the pairs of equivalent fractions?
(i) 56 and 202456 and 2024
(ii) 38 and 154038 and 1540
(iii) 47 and 162147 and 1621
(iv) 29 and 146329 and 1463
(v) 13 and 92413 and 924
(vi) 23 and 332223 and 3322
ANSWER:
The pairs of equivalent fractions are as follows:
(i) 56 and 2024 (2024 = 5×46×4)56 and 2024 2024 = 5×46×4
(ii) 38 and 1540 (1540 = 3×58×5)38 and 1540 1540 = 3×58×5
(iv) 29 and 1463 (1463 = 2×79×7)29 and 1463 1463 = 2×79×7
Page No 89:
Question 3:
Find the equivalent fraction of 3535 having
(i) denominator 30
(ii) numerator 24
ANSWER:
(i) Let 35 = 30 35 = 30
Clearly, 30 = 5 ×× 6
So, we multiply the numerator by 6.
∴ 35 = 3×65×6= 183035 = 3×65×6= 1830
Hence, the required fraction is 18301830.
(ii) Let 35 = 24 35 = 24
Clearly, 24 = 3 ×× 8
So, we multiply the denominator by 8.
∴ 35 = 3×85×8= 244035 = 3×85×8= 2440
Hence, the required fraction is 24402440.
Page No 89:
Question 4:
Find the equivalent fraction of 5959 having
(i) denominator 54
(ii) numerator 35
ANSWER:
(i) Let 59 = 54 59 = 54
Clearly, 54 = 9 ×× 6
So, we multiply the numerator by 6.
∴ 59 = 5×69×6= 305459 = 5×69×6= 3054
Hence, the required fraction is 30543054.
(ii) Let 59 = 35 59 = 35
Clearly, 35 = 5 ×× 7
So, we multiply the denominator by 7.
∴ 59 = 5×79×7= 356359 = 5×79×7= 3563
Hence, the required fraction is 35633563.
Page No 89:
Question 5:
Find the equivalent fraction of 611611 having
(i) denominator 77
(ii) numerator 60
ANSWER:
(i) Let 611 = 77 611 = 77
Clearly, 77 = 11 ×× 7
So, we multiply the numerator by 7.
∴ 611 = 6×711×7= 4277611 = 6×711×7= 4277
Hence, the required fraction is 42774277.
(ii) Let 611 = 60 611 = 60
Clearly, 60 = 6 ×× 10
So, we multiply the denominator by 10.
∴ 611 = 6×1011×10= 60110611 = 6×1011×10= 60110
Hence, the required fraction is 6011060110.
Page No 89:
Question 6:
Find the equivalent fraction of 24302430 having numerator 4.
ANSWER:
Let 2430 = 4 2430 = 4
Clearly, 4 = 24 ÷÷ 6
So, we divide the denominator by 6.
∴ 2430 = 24÷630÷6= 452430 = 24÷630÷6= 45
Hence, the required fraction is 4545.
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Question 7:
Find the equivalent fraction of 36483648 with
(i) numerator 9
(ii) denominator 4
ANSWER:
(i) Let 3648 = 9 3648 = 9
Clearly, 9 = 36 ÷÷ 4
So, we divide the denominator by 4.
∴ 3648 = 36÷448÷4= 9123648 = 36÷448÷4= 912
Hence, the required fraction is 912912.
(ii) Let 3648 = 4 3648 = 4
Clearly, 4 = 48 ÷÷ 12
So, we divide the numerator by 12.
∴ 3648 = 36÷1248÷12= 343648 = 36÷1248÷12= 34
Hence, the required fraction is 3434.
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Question 8:
Find the equivalent fraction of 56705670 with
(i) numerator 4
(ii) denominator 10
ANSWER:
(i) Let 5670 = 4 5670 = 4
Clearly, 4 = 56 ÷÷ 14
So, we divide the denominator by 14.
∴ 5670 = 56÷1470÷14= 455670 = 56÷1470÷14= 45
Hence, the required fraction is 4545.
(ii) Let 5670 = 10 5670 = 10
Clearly, 10 = 70 ÷÷ 7
So, we divide the numerator by 7.
∴ 5670 = 56×770×7= 8105670 = 56×770×7= 810
Hence, the required fraction is 810810.
Page No 89:
Question 9:
Reduce each of the following fractions into its simplest form:
(i) 915915
(ii) 48604860
(iii) 84988498
(iv) 1506015060
(v) 72907290
ANSWER:
(i) Here, numerator = 9 and denominator = 15
Factors of 9 are 1, 3 and 9.
Factors of 15 are 1, 3, 5 and 15.
Common factors of 9 and 15 are 1 and 3.
H.C.F. of 9 and 15 is 3.
∴ 915 =9÷315÷3 = 35915 =9÷315÷3 = 35
Hence, the simplest form of 915 is 35915 is 35.
(ii) Here, numerator = 48 and denominator = 60
Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
Common factors of 48 and 60 are 1, 2, 3, 4, 6 and 12.
H.C.F. of 48 and 60 is 12.
∴ 4860 =48÷1260÷12 = 454860 =48÷1260÷12 = 45
Hence, the simplest form of 4860 is 454860 is 45.
(iii) Here, numerator = 84 and denominator = 98
Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 42 and 84.
Factors of 98 are 1, 2, 7, 14, 49 and 98.
Common factors of 84 and 98 are 1, 2, 7 and 14.
H.C.F. of 84 and 98 is 14.
∴ 8498 =84÷1498÷14 = 678498 =84÷1498÷14 = 67
Hence, the simplest form of 8498 is 678498 is 67.
(iv) Here, numerator = 150 and denominator = 60
Factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 75 and 150.
Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
Common factors of 150 and 60 are 1, 2, 3, 5, 6, 10, 15 and 30.
H.C.F. of 150 and 60 is 30.
∴ 15060 =150÷3060÷30 = 5215060 =150÷3060÷30 = 52
Hence, the simplest form of 15060 is 5215060 is 52.
(v) Here, numerator = 72 and denominator = 90
Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90.
Common factors of 72 and 90 are 1, 2, 3, 6, 9 and 18.
H.C.F. of 72 and 90 is 18.
∴ 7290 =72÷1890÷18 = 457290 =72÷1890÷18 = 45
Hence, the simplest form of 7290 is 457290 is 45.
Page No 89:
Question 10:
Show that each of the following fractions is in the simplest form:
(i) 811811
(ii) 914914
(iii) 25362536
(iv) 815815
(v) 21102110
ANSWER:
(i) Here, numerator = 8 and denominator = 11
Factors of 8 are 1, 2, 4 and 8.
Factors of 11 are 1 and 11. Common factor of 8 and 11 is 1.
Thus, H.C.F. of 8 and 11 is 1.
Hence, 811811 is the simplest form.
(ii) Here, numerator = 9 and denominator = 14
Factors of 9 are 1, 3 and 9.
Factors of 14 are 1, 2, 7 and 14. Common factor of 9 and 14 is 1.
Thus, H.C.F. of 9 and 14 is 1.
Hence, 914914 is the simplest form.
(iii) Here, numerator = 25 and denominator = 36
Factors of 25 are 1, 5 and 25.
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36. Common factor of 25 and 36 is 1.
Thus, H.C.F. of 25 and 36 is 1.
Hence, 25362536 is the simplest form.
(iv) Here, numerator = 8 and denominator = 15
Factors of 8 are 1, 2, 4 and 8.
Factors of 15 are 1, 3, 5 and 15. Common factor of 8 and 15 is 1.
Thus, H.C.F. of 8 and 15 is 1.
Hence, 815815 is the simplest form.
(v) Here, numerator = 21 and denominator = 10
Factors of 21 are 1, 3, 7 and 21.
Factors of 10 are 1, 2, 5 and 10. Common factor of 21 and 10 is 1.
Thus, H.C.F. of 21 and 10 is 1.
Hence, 21102110 is the simplest form.
Page No 90:
Question 11:
Replace by the correct number in each of the following:
(i) 27=8 27=8
(ii) 35= 3535= 35
(iii) 58=20 58=20
(iv) 4560=9 4560=9
(v) 4056= 74056= 7
(vi) 4254=7 4254=7
ANSWER:
(i) 28 (27 = 2×47×4 = 828)27 = 2×47×4 = 828
(ii) 21 (35 = 3×75×7 = 2135)35 = 3×75×7 = 2135
(iii) 32 (58 = 5×48×4 = 2032)58 = 5×48×4 = 2032
(iv) 12 (4560 = 45÷560÷5 = 912)4560 = 45÷560÷5 = 912
(v) 5 (4056 = 40÷856÷8 = 57)4056 = 40÷856÷8 = 57
(vi) 9 (4254 = 42÷654÷6 = 79)4254 = 42÷654÷6 = 79
Page No 93:
Exercise 5D
Question 1:
Define like and unlike fractions and give five examples of each.
ANSWER:
Like fractions:
Fractions having the same denominator are called like fractions.
Examples: 311, 511, 711, 911, 1011311, 511, 711, 911, 1011
Unlike fractions:
Fractions having different denominators are called unlike fractions.
Examples: 34, 45, 67, 911, 21334, 45, 67, 911, 213
Page No 93:
Question 2:
Convert 35, 710, 815 and 113035, 710, 815 and 1130 into like fractions.
ANSWER:
The given fractions are 35, 710, 815 and 1130.35, 710, 815 and 1130.
L.C.M. of 5, 10, 15 and 30 = (5 ×× 2 ×× 3) = 30
So, we convert the given fractions into equivalent fractions with 30 as the denominator.
(But, one of the fractions already has 30 as its denominator. So, there is no need to convert it into an equivalent fraction.)
Thus, we have:
35 = 3×65×6 = 1830; 710 = 7×310×3 = 2130 ; 815 = 8×215×2 = 163035 = 3×65×6 = 1830; 710 = 7×310×3 = 2130 ; 815 = 8×215×2 = 1630
Hence, the required like fractions are 1830, 2130, 1630 and 1130.1830, 2130, 1630 and 1130.
Page No 93:
Question 3:
Convert 14, 58, 712 and 132414, 58, 712 and 1324 into like fractions.
ANSWER:
The given fractions are 14, 58, 712 and 1324 .14, 58, 712 and 1324 .
L.C.M. of 4, 8, 12 and 24 = (4 ×× 2 ×× 3) = 24
So, we convert the given fractions into equivalent fractions with 24 as the denominator.
(But one of the fractions already has 24 as the denominator. So, there is no need to convert it into an equivalent fraction.)
Thus, we have:
14 = 1×64×6 = 624; 58 = 5×38×3 = 1524 ; 712 = 7×212×2 = 142414 = 1×64×6 = 624; 58 = 5×38×3 = 1524 ; 712 = 7×212×2 = 1424
Hence, the required like fractions are 624, 1524, 1424 and 1324.624, 1524, 1424 and 1324.
Page No 93:
Question 4:
Fill in the place holders with the correct symbol > or <:
(i) 89 5989 59
(ii) 910 710910 710
(iii) 37 6737 67
(iv) 1115 8151115 815
(v) 611 511611 511
(vi) 1120 17201120 1720
ANSWER:
Between two fractions with the same denominator, the one with the greater numerator is the greater of the two.
(i) >
(ii) >
(iii) <
(iv) >
(v) >
(vi) <
Page No 93:
Question 5:
Fill in the place holders with the correct symbol > or <:
(i) 34 3534 35
(ii) 78 71078 710
(iii) 411 49411 49
(iv) 811 813811 813
(v) 512 58512 58
(vi) 1114 11151114 1115
ANSWER:
Between two fractions with the same numerator, the one with the smaller denominator is the greater of the two.
(i) >
(ii) >
(iii)<
(iv) >
(v) <
(vi) >
Page No 93:
Question 6:
Compare the fractions given below:
45, 5745, 57
ANSWER:
45, 5745, 57
By cross multiplying:
5 ×× 5 = 25 and 4 ×× 7 = 28
Clearly, 28 > 25
∴∴ 45 > 5745 > 57
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Question 7:
Compare the fractions given below:
38, 5638, 56
ANSWER:
38, 5638, 56
By cross multiplying:
3 ×× 6 = 18 and 5 ×× 8 = 40
Clearly, 18 < 40
∴∴ 38 < 5638 < 56
Page No 93:
Question 8:
Compare the fractions given below:
711, 67711, 67
ANSWER:
711 , 67711 , 67
By cross multiplying:
7 ×× 7 = 49 and 11 ×× 6 = 66
Clearly, 49 < 66
∴∴ 711 < 67711 < 67
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Question 9:
Compare the fractions given below:
56, 91156, 911
ANSWER:
711 , 67711 , 67
By cross multiplying:
5 ×× 11 = 55 and 9 ×× 6 = 54
Clearly, 55 > 54
∴∴ 56 > 91156 > 911
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Question 10:
Compare the fractions given below:
23, 4923, 49
ANSWER:
711 , 67711 , 67
By cross multiplying:
2 ×× 9 = 18 and 4 ×× 3 = 12
Clearly, 18 > 12
∴∴ 23 > 4923 > 49
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Question 11:
Compare the fractions given below:
613, 34613, 34
ANSWER:
613 , 34613 , 34
By cross multiplying:
6 ×× 4 = 24 and 13 ×× 3 = 39
Clearly, 24 < 39
∴∴ 613 < 34613 < 34
Page No 93:
Question 12:
Compare the fractions given below:
34, 5634, 56
ANSWER:
613, 34613, 34
By cross multiplying:
3 ×× 6 = 18 and 4 ×× 5 = 20
Clearly, 18 < 20
∴∴ 34 < 5634 < 56
Page No 93:
Question 13:
Compare the fractions given below:
58, 71258, 712
ANSWER:
58 ,71258 ,712
By cross multiplying:
5 ×× 12 = 60 and 8 ×× 7 = 56
Clearly, 60 > 56
∴∴ 58 > 71258 > 712
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Question 14:
Compare the fractions given below:
49, 5649, 56
ANSWER:
L.C.M. of 9 and 6 = (3 ×× 3 ×× 2) = 18
Now, we convert 49 and 5649 and 56 into equivalent fractions having 18 as the denominator.
∴ 49 = 4×29×2 = 818 and 56 = 5×36×3 = 151849 = 4×29×2 = 818 and 56 = 5×36×3 = 15184949
Clearly, 818 < 1518818 < 1518
∴∴ 49 < 5649 < 56
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Question 15:
Compare the fractions given below:
45, 71045, 710
ANSWER:
L.C.M. of 5 and 10 = (5 ×× 2) = 10
Now, we convert 45 45 into an equivalent fraction having 10 as the denominator as the other fraction has already 10 as its denominator.
∴ 45 = 4×25×2 = 810 45 = 4×25×2 = 810 4949
Clearly, 810 > 710810 > 710
∴∴ 45 > 71045 > 710
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Question 16:
Compare the fractions given below:
78, 91078, 910
ANSWER:
L.C.M. of 8 and 10 = (2 ×× 5 ×× 2 ×× 2) = 40
Now, we convert 78 and 91078 and 910 into equivalent fractions having 40 as the denominator.
∴ 78 = 7×58×5 = 3540 and 910 = 9×410×4 = 3640 78 = 7×58×5 = 3540 and 910 = 9×410×4 = 3640 4949
Clearly, 3540 < 36403540 < 3640
∴∴ 78 < 91078 < 910
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Question 17:
Compare the fractions given below:
1112, 13151112, 1315
ANSWER:
L.C.M. of 12 and 15 = (2 ×× 2 ×× 3 ×× 5) = 60
Now, we convert 1112 and 13151112 and 1315 into equivalent fractions having 60 as the denominator.
∴ 1112 = 11×512×5 = 5560 and 1315 = 13×415×4 = 5260 1112 = 11×512×5 = 5560 and 1315 = 13×415×4 = 5260 4949
Clearly, 5560 > 52605560 > 5260
∴∴ 1112 > 13151112 > 1315
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Question 18:
Arrange the following fractions in ascending order:
12, 34, 56 and 7812, 34, 56 and 78
ANSWER:
The given fractions are 12, 34, 56 and 7812, 34, 56 and 78.
L.C.M. of 2, 4, 6 and 8 = (2 ×× 2 ×× 2 ×× 3) = 24
We convert each of the given fractions into an equivalent fraction with denominator 24.
Now, we have:
12 = 1×122×12 = 1224; 34 = 3×64×6 = 182456 = 5×46×4 = 2024; 78 = 7×38×3 = 212412 = 1×122×12 = 1224; 34 = 3×64×6 = 182456 = 5×46×4 = 2024; 78 = 7×38×3 = 2124
Clearly, 1224 <1824 <2024 <21241224 <1824 <2024 <2124
∴ 12 <34 <56 <7812 <34 <56 <78
Hence, the given fractions can be arranged in the ascending order as follows:
12, 34, 56, 7812, 34, 56, 78
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Question 19:
Arrange the following fractions in ascending order:
23, 56, 79 and 111823, 56, 79 and 1118
ANSWER:
The given fractions are 23, 56, 79 and 1118.23, 56, 79 and 1118.
L.C.M. of 3, 6, 9 and 18 = (3 ×× 2 ×× 3) = 18
So, we convert each of the fractions whose denominator is not equal to 18 into an equivalent fraction with denominator 18.
Now, we have:
23 = 2×63×6 = 1218; 56 = 5×36×3 = 1518; 79 = 7×29×2 = 141823 = 2×63×6 = 1218; 56 = 5×36×3 = 1518; 79 = 7×29×2 = 1418
Clearly, 1118 <1218 <1418 <15181118 <1218 <1418 <1518
∴ 1118 <23 <79 <561118 <23 <79 <56
Hence, the given fractions can be arranged in the ascending order as follows:
1118 ,23 ,79 ,561118 ,23 ,79 ,56
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Question 20:
Arrange the following fractions in ascending order:
25, 710, 1115 and 173025, 710, 1115 and 1730
ANSWER:
The given fractions are 25,710, 1115 and 1730.25,710, 1115 and 1730.
L.C.M. of 5, 10, 15 and 30 = (2 ×× 5 ×× 3) = 30 
So, we convert each of the fractions whose denominator is not equal to 30 into an equivalent fraction with denominator 30.
Now, we have:
25 = 2×65×6 = 1230; 710 = 7×310×3 = 2130; 1115 = 11×215×2 = 223025 = 2×65×6 = 1230; 710 = 7×310×3 = 2130; 1115 = 11×215×2 = 2230
Clearly, 1230 <1730 <2130 <22301230 <1730 <2130 <2230
∴ 25 <1730 <710 <111525 <1730 <710 <1115
Hence, the given fractions can be arranged in the ascending order as follows:
25, 1730, 710, 111525, 1730, 710, 1115
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Question 21:
Arrange the following fractions in ascending order:
34, 78, 1116 and 233234, 78, 1116 and 2332
ANSWER:
The given fractions are 34, 78, 1116 and 2332.34, 78, 1116 and 2332.
L.C.M. of 4, 8, 16 and 32 = (2 ⨯ 2 ⨯ 2 ⨯ 2 ⨯ 2) = 32 
So, we convert each of the fractions whose denominator is not equal to 32 into an equivalent fraction with denominator 32.
Now, we have:
34 = 3×84×8 = 2432; 78 = 7×48×4 = 2832; 1116 = 11×216×2 = 223234 = 3×84×8 = 2432; 78 = 7×48×4 = 2832; 1116 = 11×216×2 = 2232
Clearly, 2232 <2332 <2432 <28322232 <2332 <2432 <2832
∴ 1116 <2332 <34 <781116 <2332 <34 <78
Hence, the given fractions can be arranged in the ascending order as follows:
1116, 2332, 34, 781116, 2332, 34, 78
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Question 22:
Arrange the following fractions in descending order:
34, 58, 1112 and 172434, 58, 1112 and 1724
ANSWER:
The given fractions are 34, 58, 1112 and 1724.34, 58, 1112 and 1724.
L.C.M. of 4, 8, 12 and 24 = (2 ⨯ 2 ⨯ 2 ⨯ 3) = 24 
So, we convert each of the fractions whose denominator is not equal to 24 into an equivalent fraction with denominator 24.
Thus, we have;
34 = 3×64×6 = 1824; 58 = 5×38×3 = 1524; 1112 = 11×212×2 = 222434 = 3×64×6 = 1824; 58 = 5×38×3 = 1524; 1112 = 11×212×2 = 2224
Clearly, 2224 >1824 >1724 >15242224 >1824 >1724 >1524
∴ 1112 >34 >1724 >581112 >34 >1724 >58
Hence, the given fractions can be arranged in the descending order as follows:
1112, 34, 1724, 581112, 34, 1724, 58
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Question 23:
Arrange the following fractions in descending order:
79, 512, 1118 and 173679, 512, 1118 and 1736
ANSWER:
The given fractions are 79, 512, 1118 and 1736.79, 512, 1118 and 1736.
L.C.M. of 9, 12, 18 and 36 = (3 ⨯ 3 ⨯ 2 ⨯ 2) = 36 
We convert each of the fractions whose denominator is not equal to 36 into an equivalent fraction with denominator 36.
Thus, we have:
79 = 7×49×4 = 2836; 512 = 5×312×3 = 1536; 1118 = 11×218×2 = 223679 = 7×49×4 = 2836; 512 = 5×312×3 = 1536; 1118 = 11×218×2 = 2236
Clearly, 2836 >2236 >1736 >15362836 >2236 >1736 >1536
∴ 79 >1118 >1736 >51279 >1118 >1736 >512
Hence, the given fractions can be arranged in the descending order as follows:
79 ,1118,1736,51279 ,1118,1736,512
Page No 93:
Question 24:
Arrange the following fractions in descending order:
23, 35, 710 and 81523, 35, 710 and 815
ANSWER:
The given fractions are 23, 35, 710 and 815.23, 35, 710 and 815.
L.C.M. of 3, 5,10 and 15 = (2 ⨯ 3 ⨯ 5) = 30 
So, we convert each of the fractions into an equivalent fraction with denominator 30.
Thus, we have:
23 = 2×103×10 = 2030; 35 = 3×65×6 = 1830; 710 = 7×310×3 = 2130; 815 = 8×215×2 = 163023 = 2×103×10 = 2030; 35 = 3×65×6 = 1830; 710 = 7×310×3 = 2130; 815 = 8×215×2 = 1630
Clearly, 2130 >2030 >1830 >16302130 >2030 >1830 >1630
∴ 710 >23 >35 >815710 >23 >35 >815
Hence, the given fractions can be arranged in the descending order as follows:
710 ,23 ,35 ,815710 ,23 ,35 ,815
Page No 93:
Question 25:
Arrange the following fractions in descending order:
57, 914, 1721 and 314257, 914, 1721 and 3142
ANSWER:
The given fractions are 57, 914, 1721 and 3142.57, 914, 1721 and 3142.
L.C.M. of 7, 14, 21 and 42 = (2 ⨯ 3 ⨯ 7) = 42 
We convert each one of the fractions whose denominator is not equal to 42 into an equivalent fraction with denominator 42.
Thus, we have:
57 = 5×67×6 = 3042; 914 = 9×314×3 = 2742; 1721 = 17×221×2 = 344257 = 5×67×6 = 3042; 914 = 9×314×3 = 2742; 1721 = 17×221×2 = 3442
Clearly, 3442 >3142 >3042 >27423442 >3142 >3042 >2742
∴ 1721 >3142 >57 >9141721 >3142 >57 >914
Hence, the given fractions can be arranged in the descending order as follows:
1721,3142,57, 9141721,3142,57, 914
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Question 26:
Arrange the following fractions in descending order:
112, 123, 17, 19, 117, 150112, 123, 17, 19, 117, 150
ANSWER:
The given fractions are 112,123, 17, 19 , 117 and 150.112,123, 17, 19 , 117 and 150.
As the fractions have the same numerator, we can follow the rule for the comparison of such fractions.
This rule states that when two fractions have the same numerator, the fraction having the smaller denominator is the greater one.
Clearly, 17 >19 >112 >117>123>15017 >19 >112 >117>123>150
Hence, the given fractions can be arranged in the descending order as follows:
17, 19, 112, 117, 123, 15017, 19, 112, 117, 123, 150
Page No 93:
Question 27:
Arrange the following fractions in descending order:
37, 311, 35, 313, 34, 31737, 311, 35, 313, 34, 317
ANSWER:
The given fractions are 37, 311, 35, 313, 34 and 317.37, 311, 35, 313, 34 and 317.
As the fractions have the same numerator, so we can follow the rule for the comparison of such fractions.
This rule states that when two fractions have the same numerator, the fraction having the smaller denominator is the greater one.
Clearly, 34 >35 >37 >311>313>31734 >35 >37 >311>313>317
Hence, the given fractions can be arranged in the descending order as follows:
34, 35, 37, 311, 313, 31734, 35, 37, 311, 313, 317
Page No 94:
Question 28:
Lalita read 30 pages of a book containing 100 pages while Sarita read 2525 of the book. Who read more?
ANSWER:
Lalita read 30 pages of a book having 100 pages.
Sarita read 2525 of the same book.
2525 of 100 pages = 25 × 100 = 2005 = 40 pages25 × 100 = 2005 = 40 pages
Hence, Sarita read more pages than Lalita as 40 is greater than 30.
Page No 94:
Question 29:
Rafiq exercised for 2323 hour, while Rohit exercise for 3434 hour. Who exercised for a longer time?
ANSWER:
To know who exercised for a longer time, we have to compare 23 hour with 34 hour 23 hour with 34 hour .
On cross multiplying:
4 ×× 2 = 8 and 3 ×× 3 = 9
Clearly, 8 < 9
∴∴ 23 hour < 34 hour23 hour < 34 hour
Hence, Rohit exercised for a longer time.
Page No 94:
Question 30:
In a school 20 students out of 25 passed in VI A, while 24 out of 30 passed in VI B. Which section gave better result?
ANSWER:
Fraction of students who passed in VI A = 2025 = 20÷525÷5 = 452025 = 20÷525÷5 = 45
Fraction of students who passed in VI B = 2430 = 24÷630÷6 = 452430 = 24÷630÷6 = 45
In both the sections, the fraction of students who passed is the same, so both the sections have the same result.
Page No 96:
Exercise 5E
Question 1:
Find the sum:
58+1858+18
ANSWER:
The given fractions are like fractions.
We know:
Sum of like fractions = Sum of the numeratorsCommon denominatorSum of the numeratorsCommon denominator
Thus, we have:
58 + 18 = (5+1) 8 = 6 384 = 3458 + 18 = 5+1 8 = 6 384 = 34
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Question 2:
Find the sum:
49+8949+89
ANSWER:
The given fractions are like fractions.
We know:
Sum of like fractions = Sum of the numeratosCommon denominatorSum of the numeratosCommon denominator
Thus, we have:
49 + 89 = (4+8) 9 = 12493 = 43 = 11349 + 89 = 4+8 9 = 12493 = 43 = 113
Page No 96:
Question 3:
Find the sum:
135+245135+245
ANSWER:
The given fractions are like fractions.
We know:
Sum of like fractions = Sum of the numeratorsCommon denominatorSum of the numeratorsCommon denominator
Thus, we have:
135 + 245 = 85 + 145 = (8+14) 5 = 225 = 425 135 + 245 = 85 + 145 = 8+14 5 = 225 = 425
Page No 96:
Question 4:
Find the sum:
29+5629+56
ANSWER:
L.C.M. of 9 and 6 = (2 ×× 3 ×× 3) = 18
Now, we have:
29 = 2 × 29 × 2 = 418; 56 = 5 × 36 × 3 = 1518∴ 29 + 56 = 418 + 1518 = (4 + 15)18 = 1918 = 1118 29 = 2 × 29 × 2 = 418; 56 = 5 × 36 × 3 = 1518∴ 29 + 56 = 418 + 1518 = 4 + 1518 = 1918 = 1118
Page No 96:
Question 5:
Find the sum:
712+916712+916
ANSWER:
L.C.M. of 12 and 16 = (2 ×× 2 ×× 2 ×× 2 ×× 3) = 48 
Now, we have:
712 = 7 × 412 × 4 = 2848; 916 = 9 × 316 × 3 = 2748∴ 712 + 916 = 2848 + 2748 = (28 + 27)48 = 5548 = 1748 712 = 7 × 412 × 4 = 2848; 916 = 9 × 316 × 3 = 2748∴ 712 + 916 = 2848 + 2748 = 28 + 2748 = 5548 = 1748
Page No 96:
Question 6:
Find the sum:
415+1720415+1720
ANSWER:
L.C.M. of 15 and 20 = (3 ×× 5 ×× 2 ×× 2) = 60 
∴ 415 + 1720 = (16 + 51)60 {[60 ÷ 15 = 4, 4 × 4 = 16] and [60 ÷ 20 = 3, 17 × 3 = 51]} = 6760 = 1760 ∴ 415 + 1720 = 16 + 5160 60 ÷ 15 = 4, 4 × 4 = 16 and 60 ÷ 20 = 3, 17 × 3 = 51 = 6760 = 1760
Page No 96:
Question 7:
Find the sum:
234+556234+556
ANSWER:
We have: 
234 + 556 = 114 + 356 L.C.M. of 4 and 6 = (2 × 2 × 3) = 12 = (66 + 140)24 {[24 ÷ 4 = 6, 6 × 11 = 66] and [24 ÷ 6 = 4, 4 × 35 = 140]} = 2061032412 = 10312 = 8712 234 + 556 = 114 + 356 L.C.M. of 4 and 6 = (2 × 2 × 3) = 12 = 66 + 14024 24 ÷ 4 = 6, 6 × 11 = 66 and 24 ÷ 6 = 4, 4 × 35 = 140 = 2061032412 = 10312 = 8712
234+556
Page No 96:
Question 8:
Find the sum:
318+1512318+1512
ANSWER:
We have:
318 + 1512 = 258 + 1712 L.C.M. of 8 and 12 = (2 × 2 × 2 × 3) = 24 = (75 + 34)24 {[24 ÷ 8 = 3, 3 × 25 = 75] and [24 ÷ 12 = 2, 2 × 17 = 34]} = 10924 = 41324 318 + 1512 = 258 + 1712 L.C.M. of 8 and 12 = (2 × 2 × 2 × 3) = 24 = 75 + 3424 24 ÷ 8 = 3, 3 × 25 = 75 and 24 ÷ 12 = 2, 2 × 17 = 34 = 10924 = 41324
234+556
Page No 96:
Question 9:
Find the sum:
2710+38152710+3815
ANSWER:
We have:
2710 + 3815 = 2710 + 5315 L.C.M. of 10 and 15 = (2 × 3 × 5) = 30 = (81 + 106)30 {[30 ÷10 = 3, 3 × 27 = 81] and [30 ÷ 15 = 2, 2 × 53 = 106]} = 18730 = 6730 2710 + 3815 = 2710 + 5315 L.C.M. of 10 and 15 = (2 × 3 × 5) = 30 = 81 + 10630 30 ÷10 = 3, 3 × 27 = 81 and 30 ÷ 15 = 2, 2 × 53 = 106 = 18730 = 6730
234+556
Page No 96:
Question 10:
Find the sum:
323+156+2323+156+2
ANSWER:
We have:
323 + 156 + 2 = 113 + 116 + 21 L.C.M. of 3 and 6 = (2 × 3) = 6 = (22 + 11 + 12)6 {[6 ÷ 3 = 2, 2 × 11 = 22], [6 ÷ 6 =1, 1 × 11 = 11] and [6 ÷ 1 = 6, 6 × 2 = 12]} = 451562 = 152 = 712 323 + 156 + 2 = 113 + 116 + 21 L.C.M. of 3 and 6 = (2 × 3) = 6 = 22 + 11 + 126 6 ÷ 3 = 2, 2 × 11 = 22, 6 ÷ 6 =1, 1 × 11 = 11 and 6 ÷ 1 = 6, 6 × 2 = 12 = 451562 = 152 = 712
234+556
Page No 96:
Question 11:
Find the sum:
3+1415+13203+1415+1320
ANSWER:
We have:
3 + 1415 + 1320 = 31 + 1915 + 2320 L.C.M. of 15 and 20 = (2 × 2 × 3 × 5) = 60 = (180 + 76 + 69)60 {[60 ÷ 1 = 60, 60 × 3 = 180], [60 ÷ 15 = 4, 4 × 19 = 76] and [60 ÷ 20 =3, 3 × 23 = 69]} = 325656012 = 6512 = 5512 3 + 1415 + 1320 = 31 + 1915 + 2320 L.C.M. of 15 and 20 = (2 × 2 × 3 × 5) = 60 = 180 + 76 + 6960 60 ÷ 1 = 60, 60 × 3 = 180, 60 ÷ 15 = 4, 4 × 19 = 76 and 60 ÷ 20 =3, 3 × 23 = 69 = 325656012 = 6512 = 5512
234+556
Page No 96:
Question 12:
Find the sum:
313+414+616313+414+616
ANSWER:
We have:
313 + 414 + 616 = 103 + 174 + 376 L.C.M. of 3, 4 and 6 = (2 × 2 × 3) = 12 = (40 + 51 + 74)12 {[12 ÷ 3 = 4, 4 × 10 = 40], [12 ÷ 4 = 3, 3 × 17 = 51] and [12 ÷ 6 =2, 2 × 37 = 74]} = 16555124 = 554 = 1334 313 + 414 + 616 = 103 + 174 + 376 L.C.M. of 3, 4 and 6 = (2 × 2 × 3) = 12 = 40 + 51 + 7412 12 ÷ 3 = 4, 4 × 10 = 40, 12 ÷ 4 = 3, 3 × 17 = 51 and 12 ÷ 6 =2, 2 × 37 = 74 = 16555124 = 554 = 1334
234+556
Page No 96:
Question 13:
Find the sum:
23+316+429+251823+316+429+2518
ANSWER:
We have:
23 + 316 + 429 + 2518 = 23 + 196 + 389 + 4118 L.C.M. of 3, 6 and 9 = (2 × 3 × 3) = 18 = (12 + 57 + 76 + 41)18 {[18 ÷ 3 = 6, 6 × 2 = 12], [18 ÷ 6 = 3, 3 × 19 = 57], [18 ÷ 9 =2, 2 × 38 = 76] and [18 ÷ 18 = 1, 1 × 41= 41]} = 18631183 = 313 = 1013 23 + 316 + 429 + 2518 = 23 + 196 + 389 + 4118 L.C.M. of 3, 6 and 9 = (2 × 3 × 3) = 18 = 12 + 57 + 76 + 4118 18 ÷ 3 = 6, 6 × 2 = 12, 18 ÷ 6 = 3, 3 × 19 = 57, 18 ÷ 9 =2, 2 × 38 = 76 and 18 ÷ 18 = 1, 1 × 41= 41 = 18631183 = 313 = 1013
234+556
Page No 96:
Question 14:
Find the sum:
213+114+256+3712213+114+256+3712
ANSWER:
We have:
213 + 114 + 256 + 3712 = 73 + 54 + 176 + 4312 L.C.M. of 3, 4, 6 and 12 = (2 × 2 × 3) = 12 = (28 + 15 + 34 + 43)12 {[12 ÷ 3 = 4, 4 × 7 = 28], [12 ÷ 4 = 3, 3 × 5 = 15], [12 ÷ 6 =2, 2 × 17 = 34] and [12 ÷ 12 = 1, 1 × 43 = 43] } = 12010121 = 10 213 + 114 + 256 + 3712 = 73 + 54 + 176 + 4312 L.C.M. of 3, 4, 6 and 12 = (2 × 2 × 3) = 12 = 28 + 15 + 34 + 4312 12 ÷ 3 = 4, 4 × 7 = 28, 12 ÷ 4 = 3, 3 × 5 = 15, 12 ÷ 6 =2, 2 × 17 = 34 and 12 ÷ 12 = 1, 1 × 43 = 43 = 12010121 = 10
234+556
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Question 15:
Find the sum:
2+34+158+37162+34+158+3716
ANSWER:
We have:
2 + 34 + 158 + 3716 = 21 + 34 + 138 + 5516 L.C.M. of 4, 8, and 16 = (2 × 2 × 2 × 2) = 16 = (32 + 12 + 26 + 55)16 {[16 ÷ 1 = 16, 16 × 2 = 32], [16 ÷ 4 = 4, 4 × 3 = 12], [16 ÷ 8 =2, 2 × 13 = 26] and [16 ÷ 16 = 1, 1 × 55= 55]} = 12516 = 71316 2 + 34 + 158 + 3716 = 21 + 34 + 138 + 5516 L.C.M. of 4, 8, and 16 = (2 × 2 × 2 × 2) = 16 = 32 + 12 + 26 + 5516 16 ÷ 1 = 16, 16 × 2 = 32, 16 ÷ 4 = 4, 4 × 3 = 12, 16 ÷ 8 =2, 2 × 13 = 26 and 16 ÷ 16 = 1, 1 × 55= 55 = 12516 = 71316
234+556
Page No 96:
Question 16:
Rohit bought a pencil for Rs 325325 and an eraser for Rs 27102710. What is the total cost of both the articles?
ANSWER:
Total cost of both articles = Cost of pencil + Cost of eraser
Thus, we have:
Rs 325 + Rs 2710 = 175 + 2710 = (34 + 27)10 (L.C.M. of 5 and 10 = (5 × 2) = 10) = 6110 = Rs 6110 Rs 325 + Rs 2710 = 175 + 2710 = 34 + 2710 (L.C.M. of 5 and 10 = (5 × 2) = 10) = 6110 = Rs 6110
Hence, the total cost of both the articles is Rs 6110Rs 6110.
Page No 96:
Question 17:
Sohini bought 412m412m of cloth for her kurta and 223m223m of cloth for her pyjamas. Ho much cloth did she purchase in all?
ANSWER:
Total cloth purchased by Sohini = Cloth for kurta + Cloth for pyjamas
Thus, we have:
(412 + 223 ) m = (92 + 83) m (L.C.M. of 2 and 3 = (2 × 3) = 6)= ((27 + 16)6) m {[6 ÷ 2 = 3, 3 × 9 = 27] and [6 ÷ 3 = 2, 2 × 8 = 16]} = (436) m = 716 m 412 + 223 m = 92 + 83 m (L.C.M. of 2 and 3 = (2 × 3) = 6)= 27 + 166 m 6 ÷ 2 = 3, 3 × 9 = 27 and 6 ÷ 3 = 2, 2 × 8 = 16 = 436 m = 716 m
∴∴ Total length of cloth purchased = 716 m 716 m
Page No 96:
Question 18:
While coming back home from his school, Kishan covered 434434 km by rickshaw and 112112 km on foot. What is the distance of his house from the school?
ANSWER:
Distance from Kishan’s house to school = Distance covered by him by rickshaw + Distance covered by him on foot
Thus, we have:
(434 + 112 ) km = (194 + 32) km = ((19 + 6)4) km (L.C.M .of 2 and 4 = (2 ×2) = 4)= (254) km = 614km 434 + 112 km = 194 + 32 km = 19 + 64 km (L.C.M .of 2 and 4 = (2 ×2) = 4)= 254 km = 614km
Hence, the distance from Kishan’s house to school is 614 km 614 km.
Page No 96:
Question 19:
The weight of an empty gas cylinder is 16451645 kg and it contains 14231423 kg of gas. What is the weight of the cylinder filled with gas?
ANSWER:
Weight of the cylinder filled with gas = Weight of the empty cylinder + Weight of the gas inside the cylinder
Thus, we have:
(1645 + 1423 ) kg = (845 + 443) kg (L.C.M. of 5 and 3 = (3 × 5) = 15)= ((252 + 220)15) kg = (47215) kg = 31715 kg 1645 + 1423 kg = 845 + 443 kg (L.C.M. of 5 and 3 = (3 × 5) = 15)= 252 + 22015 kg = 47215 kg = 31715 kg
Hence, the weight of the cylinder filled with gas is 31715 kg31715 kg.
Page No 99:
Exercise 5F
Question 1:
Find the difference:
58−1858-18
ANSWER:
Difference of like fractions = Difference of numerator ÷÷ Common denominator
58 − 18 = (5 − 1)8 = 4182 = 1258 – 18 = 5 – 18 = 4182 = 12
Page No 99:
Question 2:
Find the difference:
712−512712-512
ANSWER:
Difference of like fractions = Difference of numerator ÷÷ Common denominator
712 − 512 = (7 − 5)12 = 21126 = 16712 – 512 = 7 – 512 = 21126 = 16
Page No 99:
Question 3:
Find the difference:
437−247437-247
ANSWER:
Difference of like fractions = Difference of numerator ÷÷ Common denominator
437 − 247 = 317 − 187 = (31 − 18)7 = 137 437 – 247 = 317 – 187 = 31 – 187 = 137
Page No 99:
Question 4:
Find the difference:
56−4956-49
ANSWER:
56 − 4956 – 49
3 6, 9 2 2, 3 3 1, 3 1, 1 3 6, 9 2 2, 3 3 1, 3 1, 1
L.C.M. of 6 and 9 = (3 ×× 2 ×× 3) = 18
Now, we have:
56 = 5 × 36 × 3 = 1518; 49 = 4 × 29 × 2 = 818∴ 56 − 49 = 1518 − 818 = (15 − 8)18 = 71856 = 5 × 36 × 3 = 1518; 49 = 4 × 29 × 2 = 818∴ 56 – 49 = 1518 – 818 = 15 – 818 = 718
Page No 99:
Question 5:
Find the difference:
12−3812-38
ANSWER:
12 − 3812 – 38
L.C.M. of 2 and 8 = (2 ×× 2 ×× 2) = 8
Now, we have:
12 = 1 × 42 × 4 = 48 ∴ 12 − 38 = 48 − 38 = (4 − 3)8 = 1812 = 1 × 42 × 4 = 48 ∴ 12 – 38 = 48 – 38 = 4 – 38 = 18
Page No 99:
Question 6:
Find the difference:
58−71258-712
ANSWER:
58 − 71258 – 712
2 8, 12 2 4, 6 2 2, 3 3 1, 3 1, 1 2 8, 12 2 4, 6 2 2, 3 3 1, 3 1, 1
L.C.M. of 8 and 12 = (2 ×× 2×× 2××3) = 24
Now, we have:
58 = 5 × 38 × 3 = 1524; 712 = 7 × 212 × 2 = 1424∴ 58 − 712 = 1524 − 1424 = (15 − 14)24 = 12458 = 5 × 38 × 3 = 1524; 712 = 7 × 212 × 2 = 1424∴ 58 – 712 = 1524 – 1424 = 15 – 1424 = 124
Page No 99:
Question 7:
Find the difference:
279−1815279-1815
ANSWER:
279 − 1815 = 259 − 2315 3 9, 15 3 3, 5 51, 5 1, 1L.C.M. of 9 and 15 =(3 × 3 × 5) = 45 ∴ 259 − 2315 = (125 − 69)45 = 56 45 = 11145 {[45 ÷ 9 = 5, 5 × 25 = 125] and [45 ÷ 15 = 3, 3 × 23 = 69]}279 – 1815 = 259 – 2315 3 9, 15 3 3, 5 51, 5 1, 1L.C.M. of 9 and 15 =(3 × 3 × 5) = 45 ∴ 259 – 2315 = 125 – 6945 = 56 45 = 11145 45 ÷ 9 = 5, 5 × 25 = 125 and 45 ÷ 15 = 3, 3 × 23 = 69
Page No 99:
Question 8:
Find the difference:
358−2512358-2512
ANSWER:
358 − 2512 = 298 − 2912 2 8, 12 2 4, 6 2 2, 3 3 1, 3 1, 1 L.C.M. of 8 and 12 =(2 × 2 × 2 × 3) = 24 ∴ 298 − 2912 = (87 − 58)24 = 29 24 = 1524 {[24 ÷ 8 = 3, 3 × 29 = 87] and [24 ÷ 12 = 2, 2 × 29 = 58]}358 – 2512 = 298 – 2912 2 8, 12 2 4, 6 2 2, 3 3 1, 3 1, 1 L.C.M. of 8 and 12 =(2 × 2 × 2 × 3) = 24 ∴ 298 – 2912 = 87 – 5824 = 29 24 = 1524 24 ÷ 8 = 3, 3 × 29 = 87 and 24 ÷ 12 = 2, 2 × 29 = 58
Page No 99:
Question 9:
Find the difference:
2310−17152310-1715
ANSWER:
2310 − 1715 = 2310 − 2215 5 10, 15 2 2, 3 3 1, 3 1, 1 L.C.M. of 10 and 15 = (2 × 3 × 5) = 30= (69 − 44)30 {[30 ÷ 10 = 3, 3 × 23 = 69] and [30 ÷ 15 = 2, 2 × 22 = 44]} = 255306 = 562310 – 1715 = 2310 – 2215 5 10, 15 2 2, 3 3 1, 3 1, 1 L.C.M. of 10 and 15 = (2 × 3 × 5) = 30= 69 – 4430 30 ÷ 10 = 3, 3 × 23 = 69 and 30 ÷ 15 = 2, 2 × 22 = 44 = 255306 = 56
Page No 99:
Question 10:
Find the difference:
623−334623-334
ANSWER:
623 − 334 = 203 − 154 L.C.M. of 3 and 4 = (2 × 2 × 3) = 12 = (80 − 45)12 {[12 ÷ 3 = 4, 4 × 20 = 80] and [12 ÷ 4 = 3, 3 × 15 = 45]}= 3512 = 21112623 – 334 = 203 – 154 L.C.M. of 3 and 4 = (2 × 2 × 3) = 12 = 80 – 4512 12 ÷ 3 = 4, 4 × 20 = 80 and 12 ÷ 4 = 3, 3 × 15 = 45= 3512 = 21112
Page No 99:
Question 11:
Find the difference:
7 − 5237 – 523
ANSWER:
7 − 523 = 71 − 173 L.C.M. of 1 and 3 = 3 = (21 − 17)3 {[3 ÷ 1 = 3, 3 × 7 = 21] and [3 ÷ 3 = 1, 1 × 17 = 17]}= 43 = 1137 – 523 = 71 – 173 L.C.M. of 1 and 3 = 3 = 21 – 173 3 ÷ 1 = 3, 3 × 7 = 21 and 3 ÷ 3 = 1, 1 × 17 = 17= 43 = 113
Page No 99:
Question 12:
Find the difference:
10 − 63810 – 638
ANSWER:
10 − 638 = 101 − 518 L.C.M. of 1 and 8 = 8 = (80 − 51)8 {[8 ÷ 1 = 8, 8 × 10 = 80] and [8 ÷ 8 = 1, 1 × 51 = 51]}= 298 = 35810 – 638 = 101 – 518 L.C.M. of 1 and 8 = 8 = 80 – 518 8 ÷ 1 = 8, 8 × 10 = 80 and 8 ÷ 8 = 1, 1 × 51 = 51= 298 = 358
Page No 99:
Question 13:
Simplify:
56−49+2356-49+23
ANSWER:
We have:
56 − 49 + 23 L.C.M. of 3, 6 and 9 =(2 × 3 × 3) = 18 = (15 − 8 + 12)18 {[18 ÷ 6 = 3, 3 × 5 = 15], [18 ÷ 9 = 2, 2 × 4 = 8] and [18 ÷ 3 = 6, 6 × 2 = 12]} = (27 − 8)18 =1918 = 1118 56 – 49 + 23 L.C.M. of 3, 6 and 9 =2 × 3 × 3 = 18 = 15 – 8 + 1218 18 ÷ 6 = 3, 3 × 5 = 15, 18 ÷ 9 = 2, 2 × 4 = 8 and 18 ÷ 3 = 6, 6 × 2 = 12 = 27 – 818 =1918 = 1118
3 3, 6, 93 1, 2, 32 1, 2, 1 1, 1, 13 3, 6, 93 1, 2, 32 1, 2, 1 1, 1, 1
Page No 99:
Question 14:
Simplify:
58+34−71258+34-712
ANSWER:
We have:
58 + 34 − 712 2 4, 8, 12 2 2, 4, 6 2 1, 2, 3 3 1, 1, 3 1,1, 1 L.C.M. of 4, 8 and 12 = (2 × 2 × 2 × 3) = 24= (15 + 18 −14)24 {[24 ÷ 8 = 3, 3 × 5 = 15], [24 ÷ 4 = 6, 6 × 3 = 18] and [24 ÷ 12 =2, 2 × 7 = 14]} = (33 − 14)24 = 1924 58 + 34 – 712 2 4, 8, 12 2 2, 4, 6 2 1, 2, 3 3 1, 1, 3 1,1, 1 L.C.M. of 4, 8 and 12 = (2 × 2 × 2 × 3) = 24= 15 + 18 -1424 24 ÷ 8 = 3, 3 × 5 = 15, 24 ÷ 4 = 6, 6 × 3 = 18 and 24 ÷ 12 =2, 2 × 7 = 14 = 33 – 1424 = 1924
234+556
Page No 99:
Question 15:
Simplify:
2+1115−592+1115-59
ANSWER:
We have: 21 + 1115 − 59 3 1, 15, 9 3 1, 5, 3 5 1, 5, 1 1, 1, 1 L.C.M. of 15 and 9 = (3 × 3 × 5) = 45 = (90 + 33 −25)45 {[45 ÷ 1 = 45, 45 × 2 = 90], [45 ÷ 15 = 3, 3 × 11 = 33] and [45 ÷ 9 =5, 5 × 5 = 25]} = (90 + 8)45 = 9845 = 2845 21 + 1115 – 59 3 1, 15, 9 3 1, 5, 3 5 1, 5, 1 1, 1, 1 L.C.M. of 15 and 9 = (3 × 3 × 5) = 45 = 90 + 33 -2545 45 ÷ 1 = 45, 45 × 2 = 90, 45 ÷ 15 = 3, 3 × 11 = 33 and 45 ÷ 9 =5, 5 × 5 = 25 = 90 + 845 = 9845 = 2845
234+556
Page No 99:
Question 16:
Simplify:
534−4512+316534-4512+316
ANSWER:
We have:
534 − 4512 + 3 16 = 234 − 5312 + 196 L.C.M. of 4, 12 and 6 = (2 × 2 × 3) = 12 2 4, 12, 6 2 2, 6, 3 3 1, 2, 3 2 1, 2, 1 1, 1, 1 = (69 − 53 + 38)12 {[12 ÷ 4 =3, 3 × 23 = 69], [12 ÷ 12 =1, 1 × 53 = 53] and [12 ÷ 6 =2, 2 × 19 = 38]} = (107 − 53)12 = 5412 =92 = 412 534 – 4512 + 3 16 = 234 – 5312 + 196 L.C.M. of 4, 12 and 6 = (2 × 2 × 3) = 12 2 4, 12, 6 2 2, 6, 3 3 1, 2, 3 2 1, 2, 1 1, 1, 1 = 69 – 53 + 3812 12 ÷ 4 =3, 3 × 23 = 69, 12 ÷ 12 =1, 1 × 53 = 53 and 12 ÷ 6 =2, 2 × 19 = 38 = 107 – 5312 = 5412 =92 = 412
234+556
Page No 99:
Question 17:
Simplify:
2+5710−314152+5710-31415
ANSWER:
We have: 2 + 5710 −3 1415 = 21 + 5710 − 5915 5 1, 10, 15 2 1, 2, 3 3 1, 1, 3 1, 1, 1 L.C.M. of 10 and 15 = (2 × 5 × 3) = 30 = (60 + 171 −118)30 {[30 ÷ 1 =30, 30 × 2 = 60], [30 ÷ 10 =3, 3 × 57 = 171] and [30 ÷ 15 =2, 2 × 59 = 118]} = (231 −118)30 = 11330 = 32330 2 + 5710 -3 1415 = 21 + 5710 – 5915 5 1, 10, 15 2 1, 2, 3 3 1, 1, 3 1, 1, 1 L.C.M. of 10 and 15 = (2 × 5 × 3) = 30 = 60 + 171 -11830 30 ÷ 1 =30, 30 × 2 = 60, 30 ÷ 10 =3, 3 × 57 = 171 and 30 ÷ 15 =2, 2 × 59 = 118 = 231 -11830 = 11330 = 32330
Page No 99:
Question 18:
Simplify:
8−312−2148-312-214
ANSWER:
We have:
8 − 312 −214 = 81 − 72 − 94 2 1, 2, 4 2 1, 1, 2 1, 1, 1 L.C.M. of 1, 2 and 4 = (2 × 2) = 4 = (32 − 14 − 9)4 {[4 ÷ 1 =4, 4 × 8 = 32], [4 ÷ 2 =2, 2 × 7 = 14] and [4 ÷ 4 =1, 1 × 9 = 9]} = (32 − 23)4 = 94 = 214 8 – 312 -214 = 81 – 72 – 94 2 1, 2, 4 2 1, 1, 2 1, 1, 1 L.C.M. of 1, 2 and 4 = (2 × 2) = 4 = 32 – 14 – 94 4 ÷ 1 =4, 4 × 8 = 32, 4 ÷ 2 =2, 2 × 7 = 14 and 4 ÷ 4 =1, 1 × 9 = 9 = 32 – 234 = 94 = 214
Page No 99:
Question 19:
Simplify:
856−338+2712856-338+2712
ANSWER:
We have:
856 − 338 + 2712 = 536 − 278 + 3112 2 6, 8, 12 2 3, 4, 6 3 3, 2, 3 2 1, 2, 1 1, 1, 1 L.C.M. of 6, 8 and 12 = (2 × 2 × 2 × 3 ) = 24 = (212 − 81 + 62)24 {[24 ÷ 6 =4, 4 × 53 = 212], [24 ÷ 8 =3, 3 × 27 = 81] and [24 ÷ 12 =2, 2 × 31 = 62]} = (274 − 81)24 = 19324 = 8124 856 – 338 + 2712 = 536 – 278 + 3112 2 6, 8, 12 2 3, 4, 6 3 3, 2, 3 2 1, 2, 1 1, 1, 1 L.C.M. of 6, 8 and 12 = (2 × 2 × 2 × 3 ) = 24 = 212 – 81 + 6224 24 ÷ 6 =4, 4 × 53 = 212, 24 ÷ 8 =3, 3 × 27 = 81 and 24 ÷ 12 =2, 2 × 31 = 62 = 274 – 8124 = 19324 = 8124
Page No 99:
Question 20:
Simplify:
616−515+313616-515+313
ANSWER:
We have:
616 − 515 + 313 = 376 − 265 + 103 2 6, 5, 33 3, 5, 3 5 1, 5, 1 1, 1, 1 L.C.M. of 6, 5 and 3 = (2 × 5 × 3) = 30 = (185 − 156 + 100)30 {[30 ÷ 6 =5, 5 × 37 = 185], [30 ÷ 5 =6, 6 × 26 = 156], and [30 ÷ 3 =10, 10 × 10 = 100]} = (285 − 156)30 = 129433010 = 4310 616 – 515 + 313 = 376 – 265 + 103 2 6, 5, 33 3, 5, 3 5 1, 5, 1 1, 1, 1 L.C.M. of 6, 5 and 3 = (2 × 5 × 3) = 30 = 185 – 156 + 10030 30 ÷ 6 =5, 5 × 37 = 185, 30 ÷ 5 =6, 6 × 26 = 156, and 30 ÷ 3 =10, 10 × 10 = 100 = 285 – 15630 = 129433010 = 4310
Page No 99:
Question 21:
Simplify:
3+115+23−7153+115+23-715
ANSWER:
We have:
3 + 115 + 23 −715 = 31 + 65 + 23 − 715 5 5, 3, 15 3 1, 3, 3 1, 1, 1 L.C.M. of 1, 5, 3 and 15 = (5 × 3 ) =15 = (45 + 18 + 10 − 7)15 {[15 ÷ 1 =15, 15 × 3 = 45], [15 ÷ 5 =3, 3 × 6 = 18], [15 ÷ 3 = 5, 5 × 2 = 10] and [15 ÷ 15 = 1, 1 × 7 = 7]} = (73 − 7)15 = 6622155 =225 = 425 3 + 115 + 23 -715 = 31 + 65 + 23 – 715 5 5, 3, 15 3 1, 3, 3 1, 1, 1 L.C.M. of 1, 5, 3 and 15 = (5 × 3 ) =15 = 45 + 18 + 10 – 715 15 ÷ 1 =15, 15 × 3 = 45, 15 ÷ 5 =3, 3 × 6 = 18, 15 ÷ 3 = 5, 5 × 2 = 10 and 15 ÷ 15 = 1, 1 × 7 = 7 = 73 – 715 = 6622155 =225 = 425
Page No 99:
Question 22:
What should be added to 923923 to get 19?
ANSWER:
Let x be added to 923923 to get 19.
∴ 923 + x = 19Thus, we have: x = 19 − 923 = 191 − 293 L.C.M. of 1 and 3 is 3. =(57 − 29)3 {[3 ÷ 1 = 3, 3 × 19 = 57] and [3 ÷ 3 = 1, 1 × 29 = 29]} = 283 = 913∴ 923 + x = 19Thus, we have: x = 19 – 923 = 191 – 293 L.C.M. of 1 and 3 is 3. =57 – 293 3 ÷ 1 = 3, 3 × 19 = 57 and 3 ÷ 3 = 1, 1 × 29 = 29 = 283 = 913923
Page No 99:
Question 23:
What should be added to 67156715 to get 815815?
ANSWER:
Let x be added to 67156715 to get 815815.
∴ 6715 + x = 815Therefore, we have: x = 815 − 6715 = 415 − 9715 L.C.M. of 5 and 15 = (5 × 3) = 15 =(123 − 97)15 {[15 ÷ 5 = 3, 3 × 41 = 123] and [15 ÷ 15 = 1, 1 × 97 = 97]} = 2615 = 11115∴ 6715 + x = 815Therefore, we have: x = 815 – 6715 = 415 – 9715 L.C.M. of 5 and 15 = 5 × 3 = 15 =123 – 9715 15 ÷ 5 = 3, 3 × 41 = 123 and 15 ÷ 15 = 1, 1 × 97 = 97 = 2615 = 11115
Page No 99:
Question 24:
Subtract the sum of 359359 and 313313 from the sum of 556556 and 419419.
ANSWER:
(556 + 419) − (359 + 313) =(356 + 379) −(329 + 103) 2 6, 9, 3 3 3, 9, 3 3 1, 3, 1 1, 1, 1 L.C.M. of 3, 6, 9 = (2 × 3 × 3) = 18 = [105 + 74] − [64 + 60]18 {[18 ÷ 6 = 3, 3 × 35 = 105] and [18 ÷ 9 = 2, 2 × 37 = 74]} {[18 ÷ 9 = 2, 2 × 32 = 64] and [18 ÷ 3 = 6, 6 × 10 = 60]} = [179] − [124]18 = 5518 = 3118 556 + 419 – 359 + 313 =356 + 379 -329 + 103 2 6, 9, 3 3 3, 9, 3 3 1, 3, 1 1, 1, 1 L.C.M. of 3, 6, 9 = 2 × 3 × 3 = 18 = 105 + 74 – 64 + 6018 18 ÷ 6 = 3, 3 × 35 = 105 and 18 ÷ 9 = 2, 2 × 37 = 74 18 ÷ 9 = 2, 2 × 32 = 64 and 18 ÷ 3 = 6, 6 × 10 = 60 = 179 – 12418 = 5518 = 3118
Page No 99:
Question 25:
Of 3434 and 5757, which is greater and by how much?
ANSWER:
Let us compare 34 and 5734 and 57.
3 ×× 7 = 21 and 4 ×× 5 = 20
Clearly, 21 > 20
∴ 34 > 5734 > 57
Required difference:
= 34 − 57 L.C.M. of 4 and 7 = (2 × 2 × 7) = 28= 21 − 2028 {[28 ÷ 4 = 7, 7 × 3 = 21] and [28 ÷ 7 = 4, 4 × 5 = 20]}= 128= 34 – 57 L.C.M. of 4 and 7 = 2 × 2 × 7 = 28= 21 – 2028 28 ÷ 4 = 7, 7 × 3 = 21 and 28 ÷ 7 = 4, 4 × 5 = 20= 128
Hence, 34 is greater than 57 by 12834 is greater than 57 by 128.
Page No 99:
Question 26:
Mrs Soni bought 712712 litres of milk. Out of this milk, 534534 litres was consumed. How much milk is left with her?
ANSWER:
Amount of milk left with Mrs. Soni = Total amount of milk bought by her −- Amount of milk consumed
∴∴ Amount of milk left with Mrs. Soni = 712 − 534 = 152 − 234 L.C.M. of 2 and 4 = (2 × 2) = 4= (30 − 23)4 {[4 ÷ 2 = 2, 2 × 15 = 30] and [4 ÷ 4 = 1, 1 × 23 = 23]} = 74 = 134 litres= 712 – 534 = 152 – 234 L.C.M. of 2 and 4 = 2 × 2 = 4= 30 – 234 4 ÷ 2 = 2, 2 × 15 = 30 and 4 ÷ 4 = 1, 1 × 23 = 23 = 74 = 134 litres
∴∴ Milk left with Mrs. Soni = 134 litres134 litres
Page No 99:
Question 27:
A film show lasted for 313313 hours. Out of his time, 134134 hours was spent on advertisements. What was the actual duration of the film?
ANSWER:
Actual duration of the film = Total duration of the show −- Time spent on advertisements
=(313 − 134) hours =(103 − 74) hours L.C.M. of 3 and 4 = (2 × 2 × 3) = 12 =(40 − 2112) hours {[12 ÷ 3 = 4, 4 × 10 = 40] and [12 ÷ 4 = 3, 3 × 7 = 21]} = (1912) hours = 1712 hours =313 – 134 hours =103 – 74 hours L.C.M. of 3 and 4 = 2 × 2 × 3 = 12 =40 – 2112 hours 12 ÷ 3 = 4, 4 × 10 = 40 and 12 ÷ 4 = 3, 3 × 7 = 21 = 1912 hours = 1712 hours
Thus, the actual duration of the film was 1712 hours1712 hours.
Page No 99:
Question 28:
In one day, a rickshaw puller earned Rs 1371213712. Out of this money, he spent Rs 56345634 on food. How much money is left with him?
ANSWER:
Money left with the rickshaw puller = Money earned by him in a day −- Money spent by him on food
= Rs (13712 − 5634) L.C.M. of 2 and 4=(2 × 2) = 4 = Rs (2752 − 2274) {[4 ÷ 2 = 2, 2 × 275 = 550] and [4 ÷ 4 = 1, 1 × 227 = 227]}= Rs (550 − 2274) = Rs (3234) = Rs 8034 = Rs 13712 – 5634 L.C.M. of 2 and 4=2 × 2 = 4 = Rs 2752 – 2274 4 ÷ 2 = 2, 2 × 275 = 550 and 4 ÷ 4 = 1, 1 × 227 = 227= Rs 550 – 2274 = Rs 3234 = Rs 8034
Hence, Rs 80348034 is left with the rickshaw puller.
Page No 99:
Question 29:
A piece of wire, 234234 metres long, broke into two pieces. One piece is 5858 metre long. How long is the other piece?
ANSWER:
The length of the other piece = (Length of the wire −- Length of one piece)
= (234 − 58) m =(114 − 58) m L.C.M. of 4 and 8 =(2 × 2 × 2) = 8 = (22 − 58) m {[8 ÷ 4 = 2, 2 × 11= 22] and [8 ÷ 8 = 1, 1 × 5 = 5]}=(178) m = 218 m = 234 – 58 m =114 – 58 m L.C.M. of 4 and 8 =2 × 2 × 2 = 8 = 22 – 58 m 8 ÷ 4 = 2, 2 × 11= 22 and 8 ÷ 8 = 1, 1 × 5 = 5=178 m = 218 m
Hence, the other piece is 218 m218 m long.
Page No 99:
Exercise 5G
Question 1:
A fraction equivalent to 3535 is
(a) 3+25+23+25+2
(b) 3−25−23-25-2
(c) 3×25×23×25×2
(d) none of these
ANSWER:
(c) 3 × 25 × 23 × 25 × 2
Page No 99:
Question 2:
A fraction equivalent to 812812 is
(a) 8+412+48+412+4
(b) 8−412−48-412-4
(c) 8÷412÷48÷412÷4
(d) none of these
ANSWER:
(c) 8 ÷ 412 ÷ 48 ÷ 412 ÷ 4
Page No 100:
Question 3:
A fraction equivalent to 24362436 is
(a) 3434
(b) 2323
(c) 8989
(d) none of these
ANSWER:
(b) 23 Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.Common factors of 24 and 36 are 1, 2, 3, 4, 6, 12.H.C.F. =12Dividing both the numerator and the denominator by 12: 2436 = 24 ÷ 1236 ÷ 12 = 23(b) 23 Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.Common factors of 24 and 36 are 1, 2, 3, 4, 6, 12.H.C.F. =12Dividing both the numerator and the denominator by 12: 2436 = 24 ÷ 1236 ÷ 12 = 23
Page No 100:
Question 4:
If 3434 is equivalent to x20x20 then the value of x is
(a) 15
(b) 18
(c)12
(d) none of these
ANSWER:
(a) 15
Explanation:
(34 = x20) We have: 20 = 4 × 5So, we have to multiply the numerator by 5. ∴ x = 3 × 5 = 1534 = x20 We have: 20 = 4 × 5So, we have to multiply the numerator by 5. ∴ x = 3 × 5 = 15
Page No 100:
Question 5:
If 45604560 is equivalent to 3x3x then the value of x is
(a) 4
(b) 5
(c) 6
(d) none of these
ANSWER:
(a) 4
Explanation:
(4560 = 3x) Now, 3 = 45 ÷15So, we have to divide the denominator by 15. ∴ x = 60 ÷ 15 = 44560 = 3x Now, 3 = 45 ÷15So, we have to divide the denominator by 15. ∴ x = 60 ÷ 15 = 4
Page No 100:
Question 6:
Which of the following are like fractions?
(a) 25, 27, 29, 21125, 27, 29, 211
(b) 23, 34, 45, 5623, 34, 45, 56
(c) 18, 38, 58, 7818, 38, 58, 78
(d) none of these
ANSWER:
(c) 18, 38, 58, 7818, 38, 58, 78
(Fractions having the same denominator are called like fractions.)
Page No 100:
Question 7:
Which of the following is a proper fraction?
(a) 5353
(b) 5
(c) 125125
(d) none of these
ANSWER:
(d) none of these
In a proper fraction, the numerator is less than the denominator.
Page No 100:
Question 8:
Which of the following is a proper fractions?
(a) 7878
(b) 178178
(c) 8787
(d) none of these
ANSWER:
(a) 7878
In a proper fraction, the numerator is less than the denominator.
Page No 100:
Question 9:
Which of the following statements is correct?
(a) 34<3534<35
(b) 34>3534>35
(c) 3434 and 3535 cannot be compared
ANSWER:
(b) 34 > 3534 > 35
Between the two fractions with the same numerator, the one with the smaller denominator is the greater.
Page No 100:
Question 10:
The smallest of the fractions 35, 23, 56, 71035, 23, 56, 710 is
(a) 2323
(b) 710710
(c) 3535
(d) 5656
ANSWER:
(c) 3535
2 5, 3, 6, 10 5 5, 3, 3, 5 3 1, 3, 3, 1 1, 1, 1, 1 2 5, 3, 6, 10 5 5, 3, 3, 5 3 1, 3, 3, 1 1, 1, 1, 1
L.C.M. of 5, 3, 6 and 10 = (2 ×× 3 ×× 5) = 30
Thus, we have:
35 = 3 × 65 × 6 = 1830 23 =2 × 103 × 10 = 2030 56 =5 × 56 × 5 = 2530 710 =7 × 310 × 3 = 2130∴ The smallest fraction = 1830 = 3535 = 3 × 65 × 6 = 1830 23 =2 × 103 × 10 = 2030 56 =5 × 56 × 5 = 2530 710 =7 × 310 × 3 = 2130∴ The smallest fraction = 1830 = 35
Page No 100:
Question 11:
The largest of the fractions 45, 47, 49, 41145, 47, 49, 411 is
(a) 411411
(b) 4545
(c) 4747
(d) 4949
ANSWER:
( b ) 4545
Among the given fractions with the same numerator, the one with the smallest denominator is the greatest.
Page No 100:
Question 12:
The smallest of the fractions 611, 711, 811, 911611, 711, 811, 911 is
(a) 611611
(b) 711711
(c) 811811
(d) 911911
ANSWER:
(a) 611611
Among like fractions, the fraction with the smallest numerator is the smallest.
Page No 100:
Question 13:
The smallest of the fractions 34, 56, 712, 2334, 56, 712, 23 is
(a) 2323
(b) 3434
(c) 5656
(d) 712712
ANSWER:
(d) 712712
Explanation:
2 4, 6, 12, 3 2 2, 3, 6, 3 3 1, 3, 3, 3 1, 1, 1, 1 2 4, 6, 12, 3 2 2, 3, 6, 3 3 1, 3, 3, 3 1, 1, 1, 1
L.C.M. of 4, 6, 12 and 3 = (2 ×× 2 ×× 3) = 12
Thus, we have:
34 = 3 × 34 × 3 = 912 56 =5 × 26 × 2 = 1012 23 =2 × 43 × 4 = 812 712Clearly, 712 is the smallest fraction.34 = 3 × 34 × 3 = 912 56 =5 × 26 × 2 = 1012 23 =2 × 43 × 4 = 812 712Clearly, 712 is the smallest fraction.
Page No 100:
Question 14:
435=?435=?
(a) 175175
(b) 235235
(c) 173173
(d) none of these
ANSWER:
(b) 235235
Page No 100:
Question 15:
347=?347=?
(a) 347347
(b) 734734
(c) 467467
(d) none of these
ANSWER:
(c) 467467
On dividing 34 by 7:
Quotient = 4
Remainder = 6
347 = 4 +67 = 467347 = 4 +67 = 467
Page No 101:
Question 16:
58+18=?58+18=?
(a) 3838
(b) 3434
(c) 6
(d) none of these
ANSWER:
(b) 3434
Explanation:Addition of like fractions = Sum of the numerators / Common denominator
= 58 + 18 = (5 + 1)8 = 6384 = 3458 + 18 = (5 + 1)8 = 6384 = 34
Page No 101:
Question 17:
58−18=?58-18=?
(a) 1414
(b) 1212
(c) 116116
(d) none of these
ANSWER:
(b) 1212
Explanation:
58 − 18 = (5 − 1)8 = 4182 = 1258 – 18 = 5 – 18 = 4182 = 12
Page No 101:
Question 18:
334−214=?334-214=?
(a) 112112
(b) 114114
(c) 1414
(d) none of these
ANSWER:
(a) 112Explanation:334 − 214⇒154 − 94⇒(15 − 9)4⇒64 = 32 = 112(a) 112Explanation:334 – 214⇒154 – 94⇒(15 – 9)4⇒64 = 32 = 112
Page No 101:
Question 19:
56+23−49=?56+23-49=?
(a) 113113
(b) 116116
(c) 119119
(d) 11181118
ANSWER:
(d) 11181118
Explanation:
3 3, 6, 9 2 1, 2, 3 3 1, 1, 3 1, 1, 1 3 3, 6, 9 2 1, 2, 3 3 1, 1, 3 1, 1, 1
56 + 23 − 49 ( L.C.M. of 3, 6 and 9 = (2 × 3 × 3) = 18) = (15 + 12 −8)18 {[18 ÷ 6 = 3, 3 × 5 = 15], [18 ÷ 3 = 6, 6 × 2 = 12] and [18 ÷ 9 = 2, 2 × 4 = 8]} = (27 − 8)18 = 1918 = 1118 56 + 23 – 49 ( L.C.M. of 3, 6 and 9 = 2 × 3 × 3 = 18) = 15 + 12 -818 18 ÷ 6 = 3, 3 × 5 = 15, 18 ÷ 3 = 6, 6 × 2 = 12 and 18 ÷ 9 = 2, 2 × 4 = 8 = 27 – 818 = 1918 = 1118
Page No 101:
Question 20:
Which is greater: 313 or 3310313 or 3310?
(a) 313313
(b) 33103310
(c) both are equal
ANSWER:
(a) 313313
Explanation:
Let us compare 313 and 3310 or 103 and 3310 313 and 3310 or 103 and 3310 .
10 ⨯ 10 = 100 and 3 ⨯ 33 = 99
Clearly, 100 > 99
∴ 103>3310 or 313 >3310103>3310 or 313 >3310
Page No 103:
Exercise 5H
Question 1:
Define a fraction. Give five examples of fractions.
ANSWER:
A fraction is defined as a number representing a part of a whole, where the whole may be a single object or a group of objects.
Examples: 57 , 85 , 23 , 43 , 4957 , 85 , 23 , 43 , 49
Page No 103:
Question 2:
What fraction of an hour is 35 minutes?
ANSWER:
An hour has 60 minutes.
∴∴ Fraction for 35 minutes = 3576012 = 7123576012 = 712
Hence, 712712 part of an hour is equal to 35 minutes.
Page No 103:
Question 3:
Find the equivalent fraction of 5/8 with denominator 56.
ANSWER:
56 = 8 ⨯ 7
So, we need to multiply the numerator by 7.
∴∴ 58 = 5 × 78 × 7 = 355658 = 5 × 78 × 7 = 3556
Hence, the required fraction is 35563556.
Page No 103:
Question 4:
Represent 235235 on the number line.
ANSWER:
Let OA = AB = BC = 1 unit
∴∴ OB = 2 units and OC = 3 units
Divide BC into 5 equal parts and take 3 parts out to reach point P.
Clearly, point P represents the number 235235.
Page No 103:
Question 5:
Find the sum 245+1310+3115245+1310+3115.
ANSWER:
We have:
245 + 1310 + 3115 = 145 + 1310 + 4615 5 5, 10, 15 2 1, 2, 3 3 1, 1, 3 1, 1, 1 L.C.M. of 5, 10 and 15 = (5 × 2 × 3) = 30 = 84 + 39 + 9230 {[30 ÷ 5 = 6, 6 × 14 = 84], [30 ÷ 10 = 3, 3 × 13 = 39] and [30 ÷ 15 = 2, 2 × 46 = 92]} = 21543306 = 436 = 716 245 + 1310 + 3115 = 145 + 1310 + 4615 5 5, 10, 15 2 1, 2, 3 3 1, 1, 3 1, 1, 1 L.C.M. of 5, 10 and 15 = 5 × 2 × 3 = 30 = 84 + 39 + 9230 30 ÷ 5 = 6, 6 × 14 = 84, 30 ÷ 10 = 3, 3 × 13 = 39 and 30 ÷ 15 = 2, 2 × 46 = 92 = 21543306 = 436 = 716
Page No 103:
Question 6:
The cost of a pen is Rs 16231623 and that of a pencil is Rs 416416.
Which costs more and by how much?
ANSWER:
Cost of a pen = Rs 1623 = Rs 503 = Rs 50 × 23 × 2 = Rs 1006Rs 1623 = Rs 503 = Rs 50 × 23 × 2 = Rs 1006
Cost of a pencil = Rs 416 = Rs 256 Rs 416 = Rs 256
1006 > 256 ∴ Rs 1623 >Rs 4161006 > 256 ∴ Rs 1623 >Rs 416
So, the cost of a pen is more than the cost of a pencil.
Difference between their costs:
= Rs (503 − 256) = Rs (100 − 256) = Rs (752562) = Rs (252) = Rs 1212 = Rs 503 – 256 = Rs 100 – 256 = Rs 752562 = Rs 252 = Rs 1212
Hence, the cost of a pen is Rs 12121212 more than the cost of a pencil.
Page No 103:
Question 7:
Of 3434 and 5757, which is greater and by how much?
ANSWER:
Let us compare 34 and 5734 and 57.
By cross multiplying:
3 ⨯ 7 = 21 and 4 ⨯ 5 = 20
Clearly, 21 > 20
∴34>5734>57
Their difference:
34 − 57 L.C.M. of 4 and 7 = (2 × 2 × 7) = 28= 21 − 2028 {[28 ÷ 4 = 7, 7 × 3 = 21] and [28 ÷ 7 = 4, 4 × 5 = 20]}= 128 34 – 57 L.C.M. of 4 and 7 = 2 × 2 × 7 = 28= 21 – 2028 28 ÷ 4 = 7, 7 × 3 = 21 and 28 ÷ 7 = 4, 4 × 5 = 20= 128
Hence, 34 is greater than 57 by 128.34 is greater than 57 by 128.
Page No 103:
Question 8:
Convert the fractions 12, 23, 4912, 23, 49 and 5656 into like fractions.
ANSWER:
The given fractions are 12, 23, 49, 56. The given fractions are 12, 23, 49, 56.
L.C.M. of 2, 3, 9 and 6 = (2 ⨯ 3 ⨯ 3) = 18
Now, we have:
12 = 1 × 92 × 9 = 918 23 = 2 × 63 × 6 = 121849 = 4 × 29 × 2 = 818 56 = 5 × 36 × 3 = 1518Hence, 918, 1218, 818 and 1518 are like fractions.12 = 1 × 92 × 9 = 918 23 = 2 × 63 × 6 = 121849 = 4 × 29 × 2 = 818 56 = 5 × 36 × 3 = 1518Hence, 918, 1218, 818 and 1518 are like fractions.
Page No 103:
Question 9:
Find the equivalent fraction of 3535 having denominator 30.
ANSWER:
Let 35 = 30Let 35 = 30
30 = 5 ⨯ 6
So, we have to multiply the numerator by 6 to get the equivalent fraction having denominator 30.
∴ 35 = 3 × 65 × 6 = 183035 = 3 × 65 × 6 = 1830
Thus, 1830 is the equivalent fraction of 35.1830 is the equivalent fraction of 35.
Page No 103:
Question 10:
Reduce 84988498 to the simplest form.
ANSWER:
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
The factors of 98 are 1, 2, 7, 14, 49, 98.
The common factors of 84 and 98 are 1, 2, 7, 14.
The H.C.F. of 84 and 98 is 14.
Dividing both the numerator and the denominator by the H.C.F.:
8498 = 84 ÷ 1498 ÷ 14 = 678498 = 84 ÷ 1498 ÷ 14 = 67
Page No 103:
Question 11:
24112411 is an example of
(a) a proper fraction
(b) an improper fraction
(c) a mixed fraction
(d) none of these
ANSWER:
(b) an improper fraction
In an improper fraction, the numerator is greater than the denominator.
Page No 103:
Question 12:
3838 is an example of
(a) a proper fraction
(b) an improper fraction
(c) a mixed fraction
(d) none of these
ANSWER:
(a) proper fraction
In a proper fraction, the numerator is less than the denominator.
Page No 103:
Question 13:
3838 and 512512 on comparison give
(a) 38>51238>512
(b) 38<51238<512
(c) 38=51238=512
(d) none of these
ANSWER:
(b) 38<51238<512
Considering 38 and 51238 and 512:
On cross multiplying, we get:3 × 12 = 36 and 8 × 5 = 40Clearly, 36 < 40∴ 38 < 512On cross multiplying, we get:3 × 12 = 36 and 8 × 5 = 40Clearly, 36 < 40∴ 38 < 512
Page No 103:
Question 14:
The largest of the fractions 23, 59, 1223, 59, 12 and 712712 is
(a) 2323
(b) 5959
(c) 712712
(d) 1212
ANSWER:
(a) 2323
Explanation:
L.C.M. of 3, 9, 2 and 12 = ( 2 ⨯ 2 ⨯ 3 ⨯ 3) = 36
Now, we have:
23 = 2 × 123 × 12 = 2436 59 = 5 × 49 × 4 = 203612 = 1 × 182 × 18 = 1836 712 = 7 × 312 × 3 = 2136Hence, 2436 = 23 is the largest fraction.23 = 2 × 123 × 12 = 2436 59 = 5 × 49 × 4 = 203612 = 1 × 182 × 18 = 1836 712 = 7 × 312 × 3 = 2136Hence, 2436 = 23 is the largest fraction.
Page No 103:
Question 15:
334−112=?334-112=?
(a) 212212
(b) 214214
(c) 112112
(d) 114114
ANSWER:
(b) 214214
Explanation:
334 − 112 = 154 − 32 (L.C.M. of 2 and 4 = (2 × 2) = 4) = 15 − 64 = 94 = 214334 – 112 = 154 – 32 (L.C.M. of 2 and 4 = 2 × 2 = 4) = 15 – 64 = 94 = 214
Page No 103:
Question 16:
Which of the following are like fractions?
(a) 23, 34, 45, 5623, 34, 45, 56
(b) 25, 27, 29, 21125, 27, 29, 211
(c) 18, 38, 58, 7818, 38, 58, 78
(d) none of these
ANSWER:
(c) 18, 38, 58, 7818, 38, 58, 78
Like fractions have same the denominator.
Page No 104:
Question 17:
?−821=821?-821=821
(a) 0
(b) 1
(c) 218218
(d) 16211621
ANSWER:
(d) 16211621
? − 821 = 821? = 821 + 821 = 1621? – 821 = 821? = 821 + 821 = 1621
Page No 104:
Question 18:
Fill in the blanks:
(i) 923+……=19923+……=19
(ii) 616−?=2930616-?=2930
(iii) 7 − 523=……7 – 523=……
(iv) 72907290 reduced to simples form is ……
(v) 4254=7 4254=7
ANSWER:
(i) 923 +……=19……=19 − 923 ……= 191 − 293 ……=57 − 293 ……= 283 …..= 913(i) 923 +……=19……=19 – 923 ……= 191 – 293 ……=57 – 293 ……= 283 …..= 913
(ii)
616− ? =2930 ? = 616 − 2930 ? = 376 − 2930 ? = 185 − 2930 ? = 15626305 ? = 515616- ? =2930 ? = 616 – 2930 ? = 376 – 2930 ? = 185 – 2930 ? = 15626305 ? = 515
(iii)
7 − 523 = 71 − 173 = 21 −173 = 43 = 1137 – 523 = 71 – 173 = 21 -173 = 43 = 113
(iv)
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.The common factors of 72 and 90 are 1, 2, 3, 6, 9, 18.H.C.F. of 72 and 90 is 18. 72 ÷ 1890 ÷ 18 = 45The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.The common factors of 72 and 90 are 1, 2, 3, 6, 9, 18.H.C.F. of 72 and 90 is 18. 72 ÷ 1890 ÷ 18 = 45
(v)
4254 =79⇒42 ÷ 654 ÷ 6 = 794254 =79⇒42 ÷ 654 ÷ 6 = 79
Page No 104:
Question 19:
Write ‘T’ for true and ‘F’ for false for each of the statements given below:
(a) 313>3310313>3310.
(b) 8−156=7168-156=716.
(c) 12, 1312, 13and 1414 are like fractions.
(d) 3535 lies between 3 and 5.
(e) Among 12, 13, 34, 4312, 13, 34, 43 the largest fractions is 4343.
ANSWER:
(a) T
(b) F (81 − 116 = 48 −116 = 376 = 616)81 – 116 = 48 -116 = 376 = 616
(c) F (Because like fractions have the same denominator.)
(d) F (It lies between 0 and 1 as all proper fractions are less than 1.)
(e) T (Because it is an improper fraction, while the others are proper fractions.)
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