Worksheet on Operations on Rational Expressions

Practice the questions given in the worksheet on operations on rational expressions. The questions are related to the operations of addition, subtraction, multiplication and division on rational numbers.

1. Simplify the following rational numbers:

(i) (25/8 × 2/5) – (3/5 × -10/9)

(ii) (1/2 × ¼) + (1/2 × 6)

(iii) (-5 × 2/15) – (-6 × 2/9)

(iv) (-9/4 × 5/3) + (13/2 × 5/6)

2. Simplify the rational expressions:

(i) (3/2 × 1/6) + (5/3 × 7/2) – (13/8 × 4/3)

(ii) (1/4 × 2/7) – (5/14 × -2/3) + (3/7 × 9/2)

(iii) (13/9 × -15/2) + (7/3 × 8/5) + (3/5 × ½)

(iv) (3/11 × 5/6) – (9/12 × 4/3) + (5/13 × 6/15)

3. Find the value and express as a rational number in standard form:

(i) 2/5 ÷ 26/15

(ii) 10/3 ÷ (-35/12)

(iii) -6 ÷ (-8/17)

(iv) 40/98 ÷ (-20)

4. By what number should we multiply -15/28, so that the product may be -5/7?

5. By what number should we multiply -8/13, so that the product may be 24?

6. By what number should -3/4 be multiplied in order to produce 2/3?

7. Find (m + n) ÷ (m – n), if

(i) m = 2/3, n = 3/2

(ii) m = 2/5, n = 1/2

(iii) m = 5/4, y = -1/3

8. The cost of 7 2/3 meters of rope is $12 3/4. Find its cost per meter.

9. The cost of 2 1/3 meters of rope is $75 1/4. Find cost of cloth per meter.

10. Divide the sum of -13/5 and 12/7 by the product of -31/7 and -1/2.

11. Divide the sum of 65/12 and 8/3 by their difference.

12. If 24 trousers of equal size can be prepared in 54 meters of cloth, what length of the cloth is required for each trouser?

13. Divide the sum of 13/5 and -12/7 by the product of -31/7 and 1/-2.

14. Divide the sum of 65/12 and 8/3 by their difference.

Answers for the worksheet on operations on rational expressions are given below to check the exact answers of the above questions on rational numbers.

Answer:

1. (i) 23/12

(ii) 25/8

(iii) 2/3

(iv)5/3

2. (i) 47/12

(ii) 47/21

(iii) -34/5

(iv) -177/286

3. (i) 3/13

(ii) -8/7

(iii) 51/4

(iv) -1/49

4. 4/3

5. -39

6. -8/9

7. (i) -13/5

(ii) -9

(iii) 11/19

8. $1 61/92

9. $32 1/4

10. -2/5

11. 97/33

12. 9/4 meters

13. 2/5

14. 97/33

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