How to divide by a fraction using bar models

Dividing by a fraction tells us how many smaller parts make up a whole number or another fraction.
Bar models can help visualise the process of dividing by a fraction.
We can also use the 'invert and multiply' method to find the solution.

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Find out how to divide fractions using a bar model

Have a go

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Click to see a step-by-step slideshow.
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YOU WILL NEED: A whiteboard, ruler and coloured pens.
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STEP 1 - Draw a bar with a 3. In this example the number represents 3 litres of water.
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STEP 2 - Draw a bar and split it into the number you are dividing into. In this instance you are dividing 3 into equal sections. Write a 1 in each of the 3 sections.
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STEP 3 - Draw a second bar underneath one of the boxes and divide into two equal sections. Write a ½ in each section. These represent the ½ litre bottles of water and make up the number 1.
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STEP 4 - Repeat the bars under each section with a 1. Write a ½ in each section.
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STEP 5 - Add up how many of the smaller sections with a ½ and that's your answer! In this instance the answer is 6.

How to divide by a fraction using a bar model

Bar models can help visualise the process when you divide. To do this, you need to know your original amount, in this example it is 3, and the amount you are dividing into, in this case it's ½. A bar is then drawn to represent this amount.

The whole bar is split into single units (bars of one).

You then split each single unit into two halves.

To complete the calculation, count the total number of smaller pieces you needed for the whole bar.

Dividing by a fraction using the 'invert and multiply' method

When dividing by a fraction, we can calculate the answer using the invert and multiply method.

If the number you are dividing into is already a fraction, leave it alone. If this number is a whole number, convert it into a fraction by making the whole number the numerator (top number), and making the denominator (bottom number) '1'.
Change the division sign into a multiplication sign.
Invert the second fraction (find its reciprocal).
Multiply the numerators of the two fractions together.
Multiply the denominators of the two fractions together.
Simplify, if necessary.