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