# Equivalent Fractions

*What are called equivalent fractions?*

A given fraction and various fractions obtained by multiplying (or dividing) its numerator and denominator both by the same non-zero number, are called equivalent fractions.

In other-words:

If two or more fraction have the same value, then they are called the *equivalent* or *equal fractions*

The value of the fraction does not change if both the numerator and the denominator are multiplied by the same natural number.

(i)

^{(3 × 2)}/

_{(4 × 2)} =

^{6}/

_{8},

^{(3 × 3)}/

_{(4 × 3) } =

^{9}/

_{12},

^{(3 × 4)}/

_{(4 × 4) } =

^{12}/

_{16} etc. are equivalent fractions equivalent to the fraction

^{3}/

_{4}.

(ii)

^{1}/

_{3} =

^{(1 × 3)}/

_{(3 × 3)} =

^{3}/

_{9};

^{1}/

_{3} =

^{(1 × 6)}/

_{(3 × 6)} =

^{6}/

_{18};

^{1}/

_{3} =

^{(1 × 9)}/

_{(3 × 9)} =

^{9}/

_{27} and so on.

So,

^{1}/

_{3},

^{3}/

_{9},

^{6}/

_{18},

^{9}/

_{27}, etc., are equivalent fractions.

(iii)

^{45}/

_{27} =

^{(45 ÷ 3)}/

_{(27 ÷ 3)} =

^{15}/

_{9};

^{45}/

_{27} =

^{(45 ÷ 9)}/

_{(27 ÷ 9)} = 5/3

So,

^{45}/

_{27},

^{15}/

_{9},

^{5}/

_{3}, etc., are equivalent fractions.

** We have, **
^{8}/

_{28} =

^{(8 ÷ 4)}/

_{(28 ÷ 4)} =

^{2}/

_{7} ,

^{10}/

_{35} =

^{( 10 ÷ 5)}/

_{(35 ÷ 5)} =

^{2}/

_{7}
^{8}/

_{28} and

^{10}/

_{35} are equivalent fractions equivalent to the fraction

^{2}/

_{7}
If

^{a}/

_{b} and

^{c}/

_{d} are two equivalent fractions, then

a × d = b × c

i.e.,

^{a}/

_{b} =

^{c}/

_{d} ⇔ a × d = b × c

`

● Fractions

**Fractions**

**Types of Fractions**

**Equivalent Fractions**

**Like and Unlike Fractions**

**Conversion of Fractions**

**Fraction in Lowest Terms**

**Addition and Subtraction of Fractions**

**Multiplication of Fractions**

**Division of Fractions**

● Fractions - Worksheets

**Worksheet on Fractions**

**Worksheet on Multiplication of Fractions**

**Worksheet on Division of Fractions**

**7th Grade Math Problems**

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