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

● **Rational Numbers - Worksheets**

Worksheet on Equivalent Rational Numbers

Worksheet on Lowest form of a Rational Number

Worksheet on Standard form of a Rational Number

Worksheet on Equality of Rational Numbers

Worksheet on Comparison of Rational Numbers

Worksheet on Representation of Rational Number on a Number Line

Worksheet on Adding Rational Numbers

Worksheet on Properties of Addition of Rational Numbers

Worksheet on Subtracting Rational Numbers

Worksheet on Addition and
Subtraction of Rational Number

Worksheet on Rational Expressions Involving Sum and Difference

Worksheet on Multiplication of Rational Number

Worksheet on Properties of Multiplication of Rational Numbers

Worksheet on Division of Rational Numbers

Worksheet on Properties of Division of Rational Numbers

Worksheet on Finding Rational Numbers between Two Rational Numbers

Worksheet on Word Problems on Rational Numbers

Worksheet on Operations on Rational Expressions

Objective Questions on Rational Numbers

**8th Grade Math Practice**

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● **Rational Numbers**

Introduction of Rational Numbers

Is Every Rational Number a Natural Number?

Is Every Rational Number an Integer?

Is Every Rational Number a Fraction?

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

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

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Reciprocal of a Rational Number

Rational Expressions Involving Division

Properties of Division of Rational Numbers

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