RS Agarwal Solution | Class 6th | Chapter-6 | Simplification | Edugrown
Exercise 6A
Page No 107:
Question 1:
Simplify:
21 – 12 ÷ 3 × 2
ANSWER:
Given expression:
= 21 – 12 ÷ 3 ⨯ 2
= 21 – 4 ⨯ 2 [Performing division]
= 21 – 8 [Performing multiplication]
= 13 [Performing subtraction]
Page No 107:
Question 2:
Simplify:
16 + 8 ÷ 4 – 2 × 3
ANSWER:
Given expression:
= 16 + 8 ÷ 4 – 2 ⨯ 3
= 16 + 2 – 2 ⨯ 3 [Performing division]
= 16 + 2 – 6 [Performing multiplication]
= 18 – 6 [Performing addition]
= 12 [Performing subtraction]
Page No 107:
Question 3:
Simplify:
13 – (12 – 6 ÷ 3)
ANSWER:
Given expression:
= 13 – (12 – 6 ÷ 3 )
= 13 – (12 – 2) [Performing division]
= 13 – 10 = 3 [Performing subtraction]
Page No 107:
Question 4:
Simplify:
19 – [4 + {16 – (12 – 2)}]
ANSWER:
Given expression:
= 19 – [4 + {16 – (12 – 2)}]
= 19 – [4 + {16 – 10}] [Removing parentheses]
= 19 – [4 + 6] [Removing braces]
= 19 – 10 [Removing square brackets]
= 9
Page No 107:
Question 5:
Simplify:
36 – [18 – {14 – (15 – 4 ÷2 ×2)}]
ANSWER:
Given expression:
= 36 – [18 – {14 – (15 – 4 ÷ 2 × 2)}]
= 36 – [18 – {14 – (15 – 2 × 2)}] [Performing division]
= 36 – [18 – {14 – (15 – 4)}] [Performing multiplication]
= 36 – [18 – {14 – 11}] [Removing parentheses]
= 36 – [18 – 3] [Removing braces]
= 36 – 15 [Removing square brackets]
= 21
Page No 107:
Question 6:
Simplify:
27 – [18 – {16 – (5 – ¯4 – 1)}]
ANSWER:
Given expression:
= 27 – [18 – {16 – (5 – 4-1)}]
= 27 – [18 – {16 – (5 – 3)}] [Removing bar]
= 27 – [18 – {16 – 2}] [Removing parentheses]
= 27 – [18 – 14] [Removing braces]
= 27 – 4 [Removing square brackets]
= 23
Page No 107:
Question 7:
Simplify:
445÷35 of 5+45×310-15
ANSWER:
Given expression:
= 445 ÷35 of 5 + 45×310 – 15= 445 ÷35 × 51 + 45×310 – 15 (Removing ‘of ‘)= 245 ÷31 + 45×310 – 15 =245×13 + 45×310 – 15 (Removing ‘÷’)= 85 + 45×310 – 15 (Removing ‘×’)=85 +625 – 15 (Removing ‘×’)= 40 + 6 – 525 = 41 25 = 11625
Page No 107:
Question 8:
Simplify:
(23+49) of 35 ÷ 123×114-13
ANSWER:
Given expression:
= (23 + 49) of 35 ÷123× 114 – 13 = (6 +49) of 35 ÷123× 114 – 13 (Removing parentheses)= 109×35÷123× 114 – 13 (Removing ‘of’)= 23÷53× 114 – 13 =23×35 ×54 – 13 (Removing ‘÷’ )= 25×54 – 13 = 12 – 13 (Removing ‘×’ )= (3-2)6 = 16
Page No 107:
Question 9:
Simplify:
713÷23 of 215+138÷234-112
ANSWER:
The given expression
= 713÷23 of 215 + 138 ÷234 – 112 = 223 ÷23 of 115 + 118 ÷ 114 – 32 = 223 ÷23 ×115 + 118 ÷ 114 – 32 (Removing ‘of’) =223 ÷2215 + 118 ÷ 114 – 32 = 223×1522 +118 ÷ 114 – 32 (Removing ‘÷’) = 5 + 118 × 411 – 32 (Removing ‘÷’)= 5 + 12 – 32 ( On simplifying)= 10 +1 -32 = 82 = 4
Page No 107:
Question 10:
Simplify:
517-{3310÷(245-710)}
ANSWER:
Given expression:
= 517 – {3310÷(245 – 710)}= 367 – {3310÷(145 – 710)}= 367 – {3310÷(28-710)} = 367 – {3310÷2110} (Removing parentheses)= 367 – {3310×1021} (Removing ‘÷’)= 367 – 117 (Removing braces)= 36 – 117 = 257 = 347 (Simplifying)
Page No 107:
Question 11:
Simplify:
934÷[216+{413-(112+134)}]
ANSWER:
Given expression:
= 934 ÷ [216 + {413 – (112 + 134)}] = 394 ÷ [136 + {133 – (32 + 74)}] = 394 ÷ [136 + {133 – (6+74)}] = 394 ÷ [136 + {133 – 134}] (Removing parentheses)= 394 ÷ [136 + {52 -3912}] = 394 ÷ [136 + 1312] (Removing braces)= 394 ÷ [26 +1312] = 394 ÷3912 (Removing square brackets)= 394 × 1239 = 3 (Removing ‘÷’)
Page No 107:
Question 12:
Simplify:
4110-[212-{56-(25+310-415)}]
ANSWER:
Given expression:
= 4110- [212 – {56 – (25 + 310-415)}] = 4110 – [52 – {56 – (25 + 310-415)}] = 4110 – [52 – {56 – (12 +9 – 8 30)}] = 4110 – [52 – {56 – 1330}] (Removing parentheses) = 4110 – [52 – {25 -1330}] = 4110 – [52 – 1230] (Removing braces)= 4110 – [75 -1230] = 4110 -6330 (Removing square brackets)= 123 – 6330 = 6030 = 2
Page No 107:
Question 13:
Simplify:
156+[223-{334 (345÷912)}]
ANSWER:
Given expression:
= 156+ [223 – {334 (345÷ 912)}] = 116 + [83 – {154 (195 ÷ 192)}] = 116 + [83 – {154 (195 × 219)}] = 116 + [83 – {154 × 25}] (Removing parentheses)= 116 + [83 – 32] (Removing braces) = 116 + [16 – 96] = 116 + 76 (Removing square brackets)= 186 = 3
Page No 107:
Question 14:
Simplify:
445÷{215-12(114-¯14-15)}
ANSWER:
Given expression:
= 445 ÷ {215 – 12(114 – 14 – 15)}= 245 ÷ {115 – 12(54 – 14 – 15)} = 245 ÷ {115 – 12(54 – 120)} (Removing bar) = 245 ÷ {115 – 12(25 – 120)} = 245 ÷ {115 – 12 × 2420} (Removing parentheses)=245 ÷ {115 – 1220} (Removing ‘×’) = 245 ÷ {44 – 1220} = 245÷3220 (Removing braces) = 245 × 2032 (Removing ‘÷’)= 34 × 4 = 3
Page No 107:
Question 15:
Simplify:
712-[214÷{114-12(32-¯13-16)}]
ANSWER:
Given expression:
= 712-[214÷{ 114- 12(32 – 13 – 16)}]= 152-[94÷{ 54- 12(32 – 13 – 16)}]= 152-[94÷{ 54- 12(32 – 16)}] (Removing bar) = 152-[94÷{ 54- 12(9 -16)}] = 152-[94÷{ 54- 12×43}] (Removing parentheses)= 152-[94÷{ 54- 23}] (Removing ‘×’) = 152-[94÷{ 15 – 812}] (Removing braces) =152-[94÷712] = 152-[94×127] (Removing ‘÷’)= 152 – 277 (Removing square brackets) = 105 – 5414 =5114 = 3914
Page No 108:
Exercise 6B
Question 1:
8 + 4 ÷ 2 × 5 = ?
(a) 30
(b) 50
(c) 18
(d) none of these
ANSWER:
(c ) 18
Explanation:
= 8 + 4 ÷ 2 × 5
= 8 + 2 × 5
= 8 + 10 = 18
Page No 108:
Question 2:
54 ÷ 3 of 6 + 9 = ?
(a) 117
(b) 12
(c) 65
(d) none of these
ANSWER:
( b ) 12
Explanation:
= 54 ÷ 3 of 6 + 9
= 54 ÷ (3 x 6) + 9
= 54 ÷ 18 + 9
= 3 + 9 = 12
Page No 108:
Question 3:
13 − (12 − 6 ÷ 3) = ?
(a) 11
(b) 3
(c) 73
(d) none of these
ANSWER:
(b ) 3
Explanation:
= 13 – (12 – 6 ÷ 3)
= 13 – (12 – 2)
= 13 – 10 = 3
Page No 108:
Question 4:
1001 ÷ 11 of 13 = ?
(a) 7
(b) 1183
(c) 847
(d) none of these
ANSWER:
(a ) 7
Explanation:
= 1001 ÷ 11 of 13
= 1001 ÷ ( 11 x 13)
= 1001 ÷ 143 = 7
Page No 108:
Question 5:
133 + 28 ÷ 7 − 8 × 2 = ?
(a) 7
(b) 121
(c) 30
(d) none of these
ANSWER:
(b) 121
Explanation:
Given expression:
= 133 + 28 ÷ 7 – 8 ⨯ 2
= 133 + 4 – 8 ⨯2 [Performing division]
= 133 + 4 – 16 [Performing multiplication]
= 137 – 16 [Performing addition]
= 121 [Performing subtraction]
Page No 108:
Question 6:
3640 − 14 ÷ 7 × 2 = ?
(a) 3636
(b) 1036
(c) 1819
(d) none of these
ANSWER:
(a) 3636
Explanation:
Given expression:
= 3640 – 14 ÷ 7 ⨯ 2
= 3640 – 2 ⨯2 [Performing division]
= 3640 – 4 [Performing multiplication]
= 3636 [Performing subtraction]
Page No 108:
Question 7:
100 × 10 − 100 + 2000 ÷ 100 = ?
(a) 29
(b) 920
(c) none of these
ANSWER:
(b) 920
Explanation:
Given expression:
= 100 ⨯ 10 – 100 + 2000 ÷ 100
= 100 ⨯ 10 – 100 + 20 [Performing division]
= 1000 – 100 + 20 [Performing multiplication]
= 1020 -100 [Performing addition]
= 920 [Performing subtraction]
Page No 108:
Question 8:
27 – [18 – {16 – (5 – ¯4 – 1)] = ?
(a) 25
(b) 23
(c) none of these
ANSWER:
(b) 23
Explanation:
Given expression:
= 27 – [18 – {16 – (5 – 4-1)}]
= 27 – [18 – {16 – (5 – 3)}] (Removing bar)
= 27 – [18 – {16 – 2}] (Removing parentheses)
= 27 – [18 – 14] (Removing braces)
= 27 – 4 (Removing square brackets)
= 23
Page No 108:
Question 9:
32 – [48 ÷ {36 – (27 – ¯16 – 9)}] = ?
(a) 29
(b) 52017
(c) none of these
ANSWER:
(a) 29
Explanation:
Given expression:
= 32 – [48 ÷ {36 – ( 27 – 16-9)}]
= 32 – [48 ÷ {36 – ( 27 – 7)}] (Removing bar)
= 32 – [48 ÷ {36 -20}] (Removing parentheses)
= 32 – [48 ÷ 16] (Removing braces)
= 32 – 3 (Removing square brackets)
= 29
Page No 108:
Question 10:
8 − [28 ÷ {34 − (36 − 18 ÷ 9 × 8)}] = ?
(a) 6
(b) 649
(c) none of these
ANSWER:
(a ) 6
Explanation:
Given expression:
= 8 – [28 ÷ {34 – (36 – 18 ÷ 9 × 8)}] [Performing division]
= 8 – [28 ÷ {34 – (36 – 2 × 8)}] [Performing multiplication]
= 8 – [28 ÷ {34 – (36 – 16)}]
= 8 – [28 ÷ {34 – 20}] [Removing parentheses]
= 8 – [28 ÷ 14] [Removing braces]
= 8 – 2 = 6 [Removing square brackets]
Page No 109:
Exercise 6C
Question 1:
Simplify:
16 – [11 + {8 – 6 – ¯4 – 2}]
ANSWER:
We have:
16 – [11 + {8 – (6 -4-2 )}]
= 16 – [11 + {8 – (6 – 2)}] (Removing bar)
= 16 – [11 + {8 – 4}]
= 16 – [11 + 4] (Removing barces)
= 16 – 15 (Removing square brackets)
= 1
Page No 109:
Question 2:
Simplify:
16 + 8 ÷ 4 – 2 × 3
ANSWER:
We have:
16 + 8 ÷ 4 – 2 × 3
= 16 + 2 – 2 × 3 (Division)
= 16 + 2 – 6 (Multiplication)
= 18 – 6 (Addition)
= 12
Page No 109:
Question 3:
Simplify:
36 – [18 – {14 – (15 – 4 ÷ 2 × 2)}]
ANSWER:
Given expression:
36 – [18 – {14 – (15 – 4 ÷ 2 × 2)}] [Performing division]
= 36 – [18 – {14 – (15 – 2 × 2)}] [Performing multiplication]
= 36 – [18 – {14 – (15 – 4)}]
= 36 – [18 – {14 – 11}] [Removing parentheses]
= 36 – [18 – 3] [Removing braces]
= 36 – 15 [Removing square brackets]
= 21
Page No 109:
Question 4:
15 + 5 ÷ 5 × 2 = ?
(a) 8
(b) 2
(c) 17
(d) none of these
ANSWER:
(c) 17
We have:
15 + 5 ÷ 5 x 2
= 15 +1 x 2 (Performing division)
= 15 + 2 (Performing multiplication)
= 17
Page No 109:
Question 5:
16 – 2 ÷ 7 + 6 × 2 = ?
(a) 16
(b) 14
(c) 2757
(d) none of these
ANSWER:
(c) 2757
We have:
16 – 2 ÷ 7 + 6 × 2
= 16 – (27) + 6 × 2 [Performing division]
= 16 – (27) + 12 [Performing multiplication]
= 28 – (27) [Performing addition]
= 281 -27 = (196 -2)7 = 1947 = 2757 [Performing subtraction]
Page No 109:
Question 6:
54 ÷ 3 of 6 + 9 = ?
(a) 117
(b) 12
(c) 65
(d) none of these
ANSWER:
(b)12We have:
54 ÷ 3 of 6 + 9
= 54 ÷ 18 + 9
= 3 + 9
= 12
Discover more from EduGrown School
Subscribe to get the latest posts sent to your email.