Practice the questions given in the worksheet on equality of rational numbers. We know a rational number remains unchanged if we multiply or divide its numerator and denominator by the same non- zero integer. It follows from this that a rational number can be written in several equivalent forms. Two rational numbers are said to be equivalent if one can be obtained from the other either by multiplying or by dividing its numerator and denominator by the same non-zero integer.

The questions are related to check whether the two given rational numbers are equal or not using three different methods i.e. equality of rational numbers using standard form, equality of rational numbers with common denominator and equality of rational numbers using cross multiplication.

**1.** Which of the following rational numbers are equal?

(i) -15/27 and 6/-18

(ii) -18/24 and 15/-20

(iii) -12/32 and 27/-72

(iv) -6/-18 and 11/19

**2.** If each of
the following pairs represents a pair of equivalent rational numbers, find the
values of x.

(i) 3/4 and 7/x

(ii) -5/6 and x/7

(iii) 5/7 and x/-14

(iv) 12/5 and -60/x

**3.** **Fill in the blanks so as to make the
statement true:**

(i) A number which can be expressed in the form m/n, where m and n are integers and n is not equal to zero, is called a ________.

(ii) If the integers m and n have no common divisor other than 1 and n is positive, then the rational number m/n is said to be in the ________.

(iii) Two rational numbers are said to be equal, if they have the same ________ form.

(iv) If m
is a common divisor of x and y,
then x/y = (x ÷ k)/______

(v) lf p and q are positive integers , then m/n is a ________ rational
number and m/-n is a ________ rational number.

(vi) The standard form of -1 is ________.

(vii) If m/n is a rational number, then n cannot be ________

(viii) Two rational numbers with different numerators are equal, if their numerators are in the same ________ as their denominators.

**4.** **Write whether the statement is true or false:**

(i) Every integer is a rational number.

(ii) Every rational number is a fraction.

(iii) The quotient of two
integers is always an integer.

(iv) Every fraction is a rational number.

(v) Every rational number is an integer.

(vi) Two rational numbers with different numerators cannot be equal.

(vii) 10 can be written as a
rational number with any integer as numerator.

(viii) If m/n is a rational number and k any integer, then m/n = (m × k)/(n × k)

(ix) -16/40 is equal to 14/-35

(x) 100 can be written as a
rational number with any integer as denominator.

Answers for the worksheet on equality of rational numbers are given below to check the exact answers of the above questions on whether the two given rational numbers are equal or not.

**Answers:**

**1.** (ii), (iii)

**2.** 28/3

(ii) -35/6

(iii) -10

(iv) -25

**3.** (i) rational number

(ii) standard form

(iii) standard

(iv) y ÷ k

(v) positive, negative

(vi) -1/1

(vii) zero

(viii) ratio

**4.** (i) true

(ii) false

(iii) false

(iv) true

(v) false

(vi) false

(vii) false

(viii) false

(ix) true

(x) false

● **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****From Worksheet on Equality of Rational Numbers to HOME PAGE**

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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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