How to multiply fractions by folding paper

In fractions, the denominator is the bottom number and the numerator is the top number.
When multiplying two fractions together, we are left with a fraction of a fraction.
It can be useful to visualise maths problems.

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Click to see a step-by-step slideshow.
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YOU WILL NEED: A whiteboard, coloured pens, paper and a pencil.
$STEP 1: Count the denominator on the first fraction, in this case it is 4. Fold the paper into that number of rows.$
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STEP 1: Count the denominator on the first fraction, in this case it is 4. Fold the paper into that number of rows.
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STEP 2: Fold the paper into the number of columns indicated by the second denominator. 5 in this instance.
$STEP 3: Count the number of sections you have and label them as single fractions. In this example there are 20 sections, so label each one as ¹/₂₀$
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STEP 3: Count the number of sections you have and label them as single fractions. In this example there are 20 sections, so label each one as ¹/₂₀
$STEP 4: Shade in the number of rows according to the numerator of the first fraction. In this example, 1 of the 4 rows are shaded.$
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STEP 4: Shade in the number of rows according to the numerator of the first fraction. In this example, 1 of the 4 rows are shaded.
$STEP 5: Shade in the number of columns according to the numerator of the second fraction. In this example 2 of the 5 columns are shaded.$
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STEP 5: Shade in the number of columns according to the numerator of the second fraction. In this example 2 of the 5 columns are shaded.
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STEP 6: Count how many sections overlap and are shaded twice and that's your answer. In this example it is ²/₂₀
$STEP 7: Simplify the fraction if required. In this instance it is ¹/₁₀$
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STEP 7: Simplify the fraction if required. In this instance it is ¹/₁₀

How does it work?

Using this method is a good way to visualise the multiplication of fractions.

The denominator of the first fraction tells us how many rows we need to make by folding our paper. The denominator of the second fraction tells us how many columns we need to fold.

The numerator of the first fraction tells us how many rows we should shade. The numerator of the second tells us how many columns we should shade.

Colour each section in with different colours, for each numerator.

We then need to identify the sections which have both been shaded in, and overlap. Count how many of these there are out of the total number of sections.

Example

¼ × ⅖

Fold the piece of paper into 4 rows (because the denominator of the first fraction is 4). Now fold the paper into 5 columns (because the denominator of the second fraction is 5).

Identify how many pieces you have divided the piece of paper into. Here there are 20 sections, so each section represents ¹/₂₀

Label each of the sections with ¹/₂₀

Shade in 1 of the rows (because the numerator of the first fraction is 1). Then shade in 2 of the columns (because the numeratorof the second fraction is 2).

Finally count the overlapping sections. In this example 2 sections overlap out of the 20 parts in total. This means the answer is ²/₂₀

The answer can be simplified as a fraction as ¹/₁₀

Where next?

Discover more maths topics on Bitesize.

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How does it work?

Example

¼ × ⅖

Where next?

More on Fractions