Equivalent fractions are fractions that look different but have the same value. This means they represent the same point on the number line, even though the numerator and denominator are different.

You can find equivalent fractions by multiplying or dividing the numerator and denominator by the same non-zero number. This works because you are effectively multiplying or dividing by \(1\), which does not change the value of the fraction.

$$
\frac{1}{2} = \frac{2}{4} = \frac{3}{6}
$$

In each case, both the numerator and denominator have been multiplied by the same number.

To generate an equivalent fraction, choose any integer and multiply both parts of the fraction by it.

$$
\frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20}
$$

To check whether two fractions are equivalent, you can use cross multiplication. If the cross products are equal, the fractions are equivalent.

$$
\frac{a}{b} = \frac{c}{d} \text{ if } ad = bc
$$

Another common method is simplifying. Divide the numerator and denominator by their highest common factor (HCF). If two fractions simplify to the same form, they are equivalent.

Always remember: whatever you do to the numerator, you must do to the denominator as well. Doing this keeps the value of the fraction unchanged.

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