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Fractions are equivalent if they are of equal value. Equivalent fractions can have different numerators and denominators.

Equivalent fractions can be found by:

• using a bar model or a fraction wall
• multiplying both the numerator and denominator of a fraction by the same number
• dividing both the numerator and denominator of a fraction by a common factor

Learning about common factors may be useful when finding equivalent fractions.

A fraction wall is made up of several bars, all of equal length. Each complete bar represents one whole. It can have several bars so more fractions can be compared.

To find equivalent fractions on a fraction wall:

1. Locate the fraction on the fraction wall.

2. Draw a vertical line to the right of the fraction.

3. Any equivalent fraction will be aligned to this line.

To create equivalent fractions using multiplication and division:

1. Multiply both the numerator and the denominator by the same number. An infinite number of equivalent fractions can be created this way.

2. Divide both the numerator and denominator by a common factor. There may be more than one possible common factor.

To decide if two fractions are equivalent:

1. Simplify each fraction by dividing the numerator and denominator by their highest common factor.

2. Compare the simplified fractions.

3. If they are the same, the original fractions are equivalent.

To work out the value of a missing numerator:

1. Find the multiplier or divisor by dividing the larger denominator by the smaller denominator.

2. To find the numerator for the larger denominator, multiply by the number you found.

3. To find the numerator for the smaller denominator, divide by the number you found.

To work out the value of a missing denominator:

1. Find the multiplier or divisor by dividing the larger numerator by the smaller numerator.

2. To find the denominator for the larger numerator, multiply by the number you found.

3. To find the denominator for the smaller numerator, divide by the number you found.

Try this quiz to practise finding and creating equivalent fractions.

Equivalent fractions are used in industries like architecture. Architects prepare scale models and drawings of their designs. They use equivalent fractions in a practical setting.

Equivalent fractions can also be used in cooking or baking to adjust a recipe. For example, a cupcake recipe may make enough for [24] cupcakes. A home baker may want to change that number of cupcakes to [12]. They would need to work out the fraction of each ingredient to make sure it is equivalent to the original recipe.