Worksheet on Subtracting Rational Numbers

Practice the questions given in the worksheet on subtracting rational numbers. The questions are based on subtracting rational numbers with same denominators and subtracting rational numbers with different denominators.

We know, for any two rational numbers a/b and c/d, we have a/b - c/d = a/b + (negative of c/d)

1. Subtract the first rational number from the second in each of the following:

(i) 3/8, 5/8

(ii) -7/9, 4/9

(iii) -2/11, -9/11

(iv) 11/13, -4/13

(v) 1/4, -3/8

(vi) -2/3, 5/6

(vii) -6/7, -13/14

(viii) 3/4, 5/6

2. Evaluate each of the following:

(i) 2/3 - 3/5

(ii) -4/7 - 2/(-3)

(iii) 4/7 - (-5)/(-7)

(iv) -2 - 5/9

(v) -3/-8 - (-2)/7

(vi) -4/13 - (-5)/26

(vii) -5/14 - (-2)/7

(viii) 13/15 - 12/25.

3. The sum of the two numbers is 5/9. If one of the numbers is 1/3, find the other.

4. The sum of two numbers is -1/3. If one of the numbers is -12/3, find the other.

5. The sum of the two numbers is -4/3. If one of the numbers is -5, find the other.

6. The sum of the two rational numbers is -8. If one of the numbers is -15/7, find the other.

7. What should be added to -7/8 so as to get 5/9?

8. What number should be added to -5/11 so as to get 26/33?

9. What number should be added to -5/7 to get -2/3?

10. What number should be subtracted from -5/3 to get 5/6?

11. What number should be subtracted from 3/7 to get 5/4?

12. Fill in the blanks:

(i) -4/13 - (-3)/13 = ……

(ii) (-9)/14 + …… = -1

(iii) (-7)/9 + …… = 3

(iv) …… + 15/23 = 4

Answers for the worksheet on subtracting rational numbers are given below to check the exact answers of the above questions on subtraction of two rational numbers.

Answers:

1. (i) 1/4

(ii) 11/9

(iii) -7/11

(iv) -15/13

(v) -5/8

(vi) 3/2

(vii) -1/14

(viii) 1/12

2. (i) 1/15

(ii) 2/21

(iii) -1/7

(iv) -23/9

(v) 37/56

(vi) -3/26

(vii) -1/14

(viii) 29/75

3. 2/9

4. 11/3

5. 11/3

6. -41/7

7. 103/72

8. 41/33

9. 1/21

10. -5/2

11. -23/28

12. (i) -5/26

(ii) -5/14

(iii) 34/9

(iv) 77/23

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