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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Rational Numbers

Introduction of Rational Numbers

What is Rational Numbers?

Is Every Rational Number a Natural Number?

Is Zero a Rational Number?

Is Every Rational Number an Integer?

Is Every Rational Number a Fraction?

Positive Rational Number

Negative Rational Number

Equivalent Rational Numbers

Equivalent form of Rational Numbers

Rational Number in Different Forms

Properties of Rational Numbers

Lowest form of a Rational Number

Standard form of a Rational Number

Equality of Rational Numbers using Standard Form

Equality of Rational Numbers with Common Denominator

Equality of Rational Numbers using Cross Multiplication

Comparison of Rational Numbers

Rational Numbers in Ascending Order

Rational Numbers in Descending Order

Representation of Rational Numbers on the Number Line

Rational Numbers on the Number Line

Addition of Rational Number with Same Denominator

Addition of Rational Number with Different Denominator

Addition of Rational Numbers

Properties of Addition of Rational Numbers

Subtraction of Rational Number with Same Denominator

Subtraction of Rational Number with Different Denominator

Subtraction of Rational Numbers

Properties of Subtraction of Rational Numbers

Rational Expressions Involving Addition and Subtraction

Simplify Rational Expressions Involving the Sum or Difference

Multiplication of Rational Numbers

Product of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Reciprocal of a Rational  Number

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

Rational Numbers between Two Rational Numbers

To Find Rational Numbers