Chapter -9 Rational Numbers | Class 7th |NCERT Maths Solutions | Edugrown

Ex 9.1 Class 7 Maths Question 1.
List five rational numbers between
(i) -1 and 0
(ii) -2 and -1
(iii) −45 and −23
(iv) –12 and 23
Solution:

Ex 9.1 Class 7 Maths Question 2.
Write four more rational numbers in each of the following patterns :

Solution:

Ex 9.1 Class 7 Maths Question 3.
Give four rational numbers equivalent to
(i) −27
(ii) 5−3
(iii) 49
Solution:

Ex 9.1 Class 7 Maths Question 4.
Draw the number line and represent the following rational numbers on it :
(i) 34
(ii) −58
(iii) −74
(iv) 78
Solution:
(i) In order to represent 34 on the number line, we first draw a number line and mark a point O on it to represent zero. Now, mark the point P representing 3 on the number line as shown. Now, divide the segment OP into four equal parts. Let A, B, C be the points of division so that OA = AB =BC = CP. By construction, OA is three- fourth of OP. So, A represents the rational number 34

(ii) In order to represent −58 on the number line, we first draw a number line and mark a point O on it to represent zero. Now, mark the point P representing -5 on it as shown. Now, divide the segment OP into eight equal parts. Let A, B, C, D, E, F, G be the points of division such that OA = AB = BC = CD = DE = EF = FG = GP. By construction, OA is one-eighth of OP. So, A represents the rational number −58.

(iii) In order to represent −74 on the number line, we first draw a number line and mark a point O on it to represent zero. Now, mark a point P to represent -7 on the number line. Now,divide the segment OP into 4 equal parts. Let A, B, C be the points of division so that OA = AB = BC = CP. By construction, OA is one-fourth of OP. Therefore, A represents the rational number −74.

(iv) In order to represent 78 on the number line, we first draw a number line and mark a point O on it to represent zero. Now, mark the point P to represent 7 on the number line. Now, divide the segment OP into 8 equal parts. Let A, B, C, D, E, F, G be the points of division such that OA = AB = BC = CD = DE = EF = FG = GP. By construction, OA is one-eighth of OP. Therefore, A represents the rational number 78.

Ex 9.1 Class 7 Maths Question 5.
The points P, Q, R, S, T, U, A, and B on the number line are such that, TR = RS = SU and AP = PQ = QB. Name the rational numbers represented by P, Q, R, and S.

Solution:

Ex 9.1 Class 7 Maths Question 6.
Which of the following pairs represents the same rational number?

Solution:

Ex 9.1 Class 7 Maths Question 7.
Rewrite the following rational numbers in the simplest form :
(i) −86
(ii) 2545
(iii) −4472
(iv) −810
Solution:

Ex 9.1 Class 7 Maths Question 8.
Fill in the boxes with the correct symbol out of >, <, and =.

Solution:
(i) Clearly, −57 is a negative rational number and 23 is a positive rational number. We know that every negative rational number is less than every positive rational number. Therefore,

(ii) Clearly, denominators of the given rational numbers are positive. The denominators are 5 and 7. Their L.C.M. is 35. So, we first express each rational number with 35 as a common denominator.

(iii) First- we write each one of the given rational numbers with a positive denominator.
Clearly, denominator of −78 is positive.
The denominator of 14−16 is negative.
So, we express it with a positive denominator as follows:

(iv) Clearly, the denominators of the given rational numbers are positive. The denominators are 5 and 4.
Their L.C.M. is 20. So, we first express each rational number with 20 as a common denominator.

(v) First we write each one of the given rational numbers with a positive denominator.
Clearly, denominator of 1−3 is negative.
So, expressing it with a positive denominator as follows:

(vi) First we write each one of the given rational numbers with a positive denominator.

(vii) Since every negative rational number is less than 0,

Ex 9.1 Class 7 Maths Question 9.
Which is greater in each of the following :
(i) 23,52
(ii) −56,−43
(iii) −34,2−3
(iv) −14,14
(v) -327,-345
Solution:

Ex 9.1 Class 7 Maths Question 10.
Write the following rational numbers in ascending order :

Solution:

Ex 9.2 Class 7 Maths Question 1.
Find the sum :

Solution:

Ex 9.2 Class 7 Maths Question 2.
Find :

Solution:

Ex 9.2 Class 7 Maths Question 3.
Find the product :

Solution:

Ex 9.2 Class 7 Maths Question 4.
Find the value of :

Solution: