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Year 7

Dividing a fraction by a fraction

I can use the mathematical structures that underpin the division of fractions to divide a fraction by a fraction.

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New
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Year 7

Dividing a fraction by a fraction

I can use the mathematical structures that underpin the division of fractions to divide a fraction by a fraction.

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Lesson details

Key learning points

  1. A diagram can help to show the underlying structure.
  2. Another method is the use the reciprocal of the dividing fraction.
  3. The reciprocal is the multiplicative inverse.
  4. The product of a number and its reciprocal is one.

Keywords

  • Reciprocal - A reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1

Common misconception

Numerators are divided and denominators are divided.

Emphasize the definition of division. "How many times does.... fit into it?"


To help you plan your year 7 maths lesson on: Dividing a fraction by a fraction, download all teaching resources for free and adapt to suit your pupils' needs...

In the second explanation, pupils do this together with regular checks from the teacher via MWBs (which have grids) or in student exercise books. These steps synchronously completed, emphasise how many times a fraction "fits into" another fraction.
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Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Using a bar model or otherwise, complete the statement $$ 6\div \frac{2}{5}$$ = .
Correct Answer: 15, fifteen
Q2.
Using a bar model or otherwise, complete the statement $$ 10\div \frac{2}{3}$$ = .
Correct Answer: 15, fifteen
Q3.
Without using a bar model, which calculation is the most efficient calculation to work out $$ 8\div \frac{2}{5}$$ ?
$$\frac{16}{2} \div \frac{2}{5}$$
$$\frac{24}{3} \div \frac{2}{5}$$
$$\frac{400}{50} \div \frac{2}{5}$$
Correct answer: $$\frac{40}{5} \div \frac{2}{5}$$
Q4.
Using a model or otherwise, work out the answer for $$5 \div \frac{2}{7}$$.
$$15 {{2} \over {7}}$$
$$17 {{2} \over {7}}$$
$$16 {{1} \over {2}}$$
Correct answer: $$17 {{1} \over {2}}$$
$$17 {{3} \over {4}}$$
Q5.
Here is a bar model. Three of the Oak students think they know what the question was. Which student is correct?
An image in a quiz
Sam says " It is $$6 \div \frac{3}{4}$$"
Aisha says " It is $$6 \div \frac{2}{3}$$"
Correct answer: Laura says " It is $$6 \div \frac{3}{5}$$"
Sofia says " It is $$6 \div \frac{2}{5}$$"
Q6.
Order the following from largest to smallest. Drawing bar models to find the mixed number may help.
1 - $$10 \div \frac{3}{5}$$
2 - $$2 \div \frac{2}{11}$$
3 - $$4 \div \frac{3}{4}$$
4 - $$4\div \frac{4}{5}$$
5 - $$5 \div \frac{5}{3}$$

Exit quiz

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6 Questions

Q1.
A reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to __________
Correct answer: 1
0
-1
itself
Q2.
Match the value on the left with its reciprocal on the right.
Correct Answer:$$\frac{2}{3}$$,$$\frac{3}{2}$$
tick

$$\frac{3}{2}$$

Correct Answer:$$\left(-\frac{2}{3}\right)$$,$$\left(-\frac{3}{2}\right)$$
tick

$$\left(-\frac{3}{2}\right)$$

Correct Answer:2,$$\frac{1}{2}$$
tick

$$\frac{1}{2}$$

Correct Answer:$$\frac{12}{11}$$,$$\frac{11}{12}$$
tick

$$\frac{11}{12}$$

Correct Answer:$$\frac{1}{12}$$,12
tick

12

Q3.
Which of the following is the answer to $$\frac{3}{4} \div \frac{2}{5}$$?
$$\frac{6}{20}$$
$$\frac{15}{20}$$
Correct answer: $$\frac{15}{8}$$
$$\frac{3}{4}$$
Q4.
Which of the following is the answer to $$\frac{2}{5} \div \frac{3}{7}$$?
Correct answer: $$\frac{14}{15}$$
$$\frac{15}{14}$$
$$\frac{6}{35}$$
$$\frac{35}{6}$$
Q5.
Work out the missing length given the area.
An image in a quiz
$$\frac{5}{16}$$
$$\frac{15}{48}$$
$$\frac{20}{9}$$
Correct answer: $$\frac{9}{20}$$
Q6.
Work out the missing length given the area.
An image in a quiz
$$\frac{7}{8}$$
$$\frac{4}{7}$$
Correct answer: $$\frac{7}{4}$$
$$\frac{7}{25}$$