Equivalent Rational Numbers

Equivalent rational numbers are rational numbers that have the same value but can be represented in different forms. A rational number is a number of the form p/q, where p and q are integers and q is not equal to 0. We can say that if a number can be expressed as a fraction where both the numerator and the denominator are integers, then the number is a rational number.

In this lesson, let's learn about equivalent rational numbers and how to find equivalent rational numbers using solved examples.

Two rational numbers are said to be equivalent if their lowest forms are the same. For example, 2/3 and 18/27 are equivalent because when these are reduced to their lowest forms, they give the same value. These numbers are the same as equivalent fractions, such as 1/2, 2/4, and 4/6. These are considered equivalent rational numbers.

Equivalent Rational Numbers Definition

Equivalent rational numbers are rational numbers having the same value but are often represented in different forms.

Equivalent Rational Numbers by multiplication

For a rational number a/b, consider a non zero integer m, then a × m / b × m is a rational number equivalent to a/b. Let's find the equivalent rational numbers of 2/5.

• 2 × 2 / 5 × 2 = 4/10
• 2 × 3 / 5 × 3 = 6/15
• 2 × 4 / 5 × 4 = 8/20

Therefore, the equivalent rational numbers of 2/5 are 4/10, 6/15, 8/20, and so on.

Equivalent rational numbers using Division

For a rational number a/b, consider a common divisor m, of a and b, then a ÷ m / b ÷ m is a rational number equivalent to a/b. Let's find the equivalent rational numbers of 36/72.

• 36 ÷ 2 / 72 ÷ 2 = 18/36
• 36 ÷ 3 / 72 ÷ 3 = 12/24
• 36 ÷ 4 / 72 ÷ 4 = 9/18

Therefore, the equivalent rational numbers of 36/72 are 18/36, 12/24, 9/18, and so on.

Related Articles:

Given below is a list of articles related to equivalent rational numbers.

• Rational Numbers Calculator
• Operations on Rational Numbers

What Are Equivalent Forms of Rational Numbers?

We need to multiply or divide the numerator and the denominator by the same number, in order to find the equivalent forms of rational numbers.

What Is Equivalent Rational Number Example?

We know that on multiplying the numerator and denominator of a fraction with the same integer, its value doesn't change, thus, we can find the equivalent numbers in either of the ways. For example, 3/8 and 12/32 are equivalent because 12/32 can be obtained by multiplying the numerator and the denominator of the rational number 3/8 by 4.

How Do You Know If Two Rational Numbers Are Equivalent or Not?

We know that the two rational numbers are equivalent if one can be obtained from the other either by multiplying or by dividing its numerator as well as the denominator by the same non-zero integer.

Are 14/21 and 12/15 are equivalent Rational Numbers?

Let's check by reducing them to their lowest forms.

• The common divisor of 14 and 21 is 7, thus, 14/21 can be expressed as 2/3.
• Similarly, the common divisor of 12 and 15 is 3, thus 12/15 can be expressed as 4/5.

Since the lowest forms do not represent the same value, therefore, 14/21 and 12/15 are not equivalent rational numbers.