Fractions that specify the same amount with different place values are equivalent fractions. In the set of equivalent fractions, the fractions without a common factor between numerator and denominator is the simplest form.

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The whole is split into `4` pieces and `2` pieces are considered. The fraction represented by the colored part is `2/4`

Whole is split into `2` pieces and `1` piece is considered. The fraction represented by the colored portion is `1/2`.

The picture shows three parts in three different colors.

• The gray part shows the whole

• The orange part shows the fraction `2/4`

• The purple part shows the fraction `1/2` The fraction `2/4` and `1/2` represent the same amount and the same number.

The numerator and denominator of one fraction is a multiple of numerator and denominator of another fraction respectively. Such fractions are called equivalent fractions.

The word "equivalent" means equal in value or amount. The equivalent fractions are fraction of equal amount.

*familiarize with the terminology *

equivalent fractions

The picture shows four fractions , `1/2`, `2/4`, `3/6`, and `4/8`. These are equivalent fractions.

The fractions `2/4`, `3/6`, and `4/8` have numerator and denominator with common factors `2`, `3` and `4` respectively.

Only the fraction `1/2` has no common factor between numerator and denominator. A fraction without a common factor between the numerator and the denominator is the simplest form of the equivalent fractions.

The word "simplest" means: without complexity, plain, simple and elementary. A fraction without a common factor between the numerator and the denominator is the simplest form of the equivalent fractions.

*familiarize with the terminology *

simplest form

Fractions that specify the same amount with different place values are equivalent fractions.

The fraction that specifies the same amount with lowest denominator possible is the simplest form of equivalent fractions.

**Equivalent Fraction:** Two fractions `p/q` and `l/m` are equivalent if the numerators `l`, `p` and the denominators `m`, `q` have a common factor `a`. That is `l = a xx p` and `m = a xx q`. `a` is an integer. Note that, `l/m` and `p/q` specify the same amount with different place values.

**Simplest Form of a fraction: ** A fraction `p/q` without a common factor between the numerator and the denominator is the simplest form of the equivalent fractions. That is, `p != a xx q` for any integer `a`.

*Solved Exercise Problem: *

Given fractions `1/2`and `2/4`. Which one is the simplest form of the given equivalent fractions?

- The given fractions are not equivalent
- `1/4`
- `1/2`
- `1/2`
- `2/4`

The answer is '`1/2`'.

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