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.

Find out how to divide fractions using a bar model

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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.

  1. 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'.
  2. Change the division sign into a multiplication sign.
  3. Invert the second fraction (find its reciprocal).
  4. Multiply the numerators of the two fractions together.
  5. Multiply the denominators of the two fractions together.
  6. Simplify, if necessary.

Example 1

3 ÷ ¹/₂ = ?

Convert '3' into a fraction. Change '÷' to 'x'. Invert the second fraction.

³/₁ x ²/₁ = ⁶/₁ = 6

Example 2

5 ÷ ¹/₃ = ?

Convert '5' into a fraction. Change '÷' to 'x'. Invert the second fraction.

⁵/₁ x ³/₁ = ¹⁵/₁ = 15

Where next?

Discover more about this topic from around Bitesize.

How to work out a fraction of an amount
How to turn a fraction into a percentage
What is a factor?