# Equivalent Fractions

Equivalent fractions are the fractions having the same value.

We have,

2/4 = (1 × 2)/(2 × 2)

3/6 = (1 × 3)/(2 × 3)

4/8 = (1 × 4)/(2 × 4)

We observe that 2/4, 3/6 and 4/8 are obtained by multiplying the numerator and denominator of 1/2 by 2, 3 and 4 respectively.

Thus, an equivalent fraction of a given fraction can be obtained by multiplying its numerator and denominator by the same number (other than zero).

2/4 = (2÷ 2)/(4 ÷ 2) = 1/2

3/6 = (3÷ 3)/(6 ÷ 3) = 1/2

4/8 = (4 ÷ 4)/(8 ÷ 4) = 1/2

We observe that if we divide the numerators and denominators of 2/4, 3/6 and 4/8 each by their common factor 2, we get an equivalent fraction 1/2.

Thus, an equivalent fraction of a given fraction can be obtained by dividing its numerator and denominator by their common factor (other than 1), if ant.

Note:

(i) Multiplying its numerator (top) and denominator (bottom) by the same number (other than 0).

(ii) Dividing its numerator (top) and denominator (bottom) by their common factor (other than 1).

For Example:

1. Write three equivalent fraction of 3/5.

Equivalent fractions of 3/5 are:

(3 × 2)/(5× 2) = 6/10,

(3 × 3)/(5 × 3) = 9/15,

(3 × 4)/(5 × 4) = 12/20

Therefore, equivalent fractions of 3/5 are 6/10, 9/15 and 12/20.

2. Write three equivalent fraction of 2/3.

Equivalent fractions of 2/3 are:

(2× 2)/(3× 2) = 4/6,

(2 × 3)/(3 × 3) = 6/9,

(2× 4)/(3× 4) = 8/12

Therefore, equivalent fractions of 2/3 are 4/6, 6/9 and 8/12.

3. Write three equivalent fraction of 1/4.

Equivalent fractions of 1/4 are:

(1× 2)/(4× 2) = 2/8,

(1 × 3)/(4 × 3) = 3/12,

(1× 4)/(4× 4) = 4/16

Therefore, equivalent fractions of 1/4 are 2/8, 3/12 and 4/16.

4. Write three equivalent fraction of 2/15.

Equivalent fractions of 2/15 are:

(2× 2)/(15 × 2) = 4/30,

(2 × 3)/(15 × 3) = 6/45,

(2× 4)/(15 × 4) = 8/60

Therefore, equivalent fractions of 2/15 are 4/30, 6/45 and 8/60.

5. Write three equivalent fraction of 3/10.

Equivalent fractions of 3/10 are:

(3× 2)/(10× 2) = 6/20,

(3 × 3)/(10 × 3) = 9/30,

(3× 4)/(10× 4) = 12/40

Therefore, equivalent fractions of 3/10 are 6/20, 9/30 and 12/40.

Representations of Fractions on a Number Line

Fraction as Division

Types of Fractions

Conversion of Mixed Fractions into Improper Fractions

Conversion of Improper Fractions into Mixed Fractions

Equivalent Fractions

Fractions in Lowest Terms

Like and Unlike Fractions

Comparing Like Fractions

Comparing Unlike Fractions

Addition and Subtraction of Like Fractions

Addition and Subtraction of Unlike Fractions

Inserting a Fraction between Two Given Fractions