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5. Equivalent fractions and standard form of rational numbers

Equivalent fractions:

Fractions like

\frac{1}{2}, \frac{2}{4}, \frac{3}{6}, \frac{4}{8}

have a different numerator and different denominator but represent the same value. These are called equivalent fractions. To find the equivalent fraction of a given fraction, multiply numerator and denominator by the same number.

Example:

\(1/5\) can be converted into its equivalent fraction as,

\frac{1 \times 2}{5 \times 2} = \frac{2}{10}; \frac{1 \times 3}{5 \times 3} = \frac{3}{15}

The standard form of rational numbers:

A rational number

\frac{p}{q}

is in standard form if its denominator is positive and the common factor between numerator and denominator should be \(1\).

Steps to convert rational numbers into the standard form:

1. A rational number in the standard form, it will not have a negative sign in the denominator, so

\frac{p}{- q}

should be taken as

\frac{- p}{q}

2. Divide the numerator \(p\) and denominator \(q\) by their HCF (Highest Common Factor).

Example:

Write

\frac{12}{- 8}

in standard form.

1. Take the negative sign from denominator to the numerator,

\frac{- 12}{8}

2.HCF (Highest Common Factor) of numerator \(12\) and denominator \(8\) is \(4\). Divide numerator \(12\) and denominator \(8\) by \(4\) which is equal to

\frac{- 3}{2}

that is

\frac{- 12 \div 4}{8 \div 4} = \frac{- 3}{2}

Thus, the standard form of

\frac{- 12}{8}

\frac{- 3}{2}

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5. Equivalent fractions and standard form of rational numbers

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