Skip to content
Teachers
Go to pupils
Choose exam board for KS4 Biology
Choose exam board for KS4 Chemistry
Choose exam board for KS4 Combined science
Choose exam board for KS4 Computer Science (GCSE)
Choose exam board for KS4 English
Choose exam board for KS4 French
Choose exam board for KS4 Geography
Choose exam board for KS4 German
Choose exam board for KS4 History
Choose tier for KS4 Maths
Choose exam board for KS4 Music
Choose exam board for KS4 Physical education (GCSE)
Choose exam board for KS4 Physics
Choose exam board for KS4 Religious education (GCSE)
Choose exam board for KS4 Spanish

Guidance

About us

Dividing a fraction by a fraction

Download all resources
Previous lesson
Next lesson
Skip to lesson content
Share lesson with pupils

Lesson details

Learning outcome

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

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?"

Teacher tip

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.

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

Skip lesson video

Loading...

Prior knowledge starter quiz

Download starter quiz questions (PDF)

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 - $$5 \div \frac{5}{3}$$

Assessment exit quiz

Download exit quiz questions (PDF)

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:$$\frac{2}{3}$$,$$\frac{3}{2}$$

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

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

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

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

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

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

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

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

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: $$\frac{7}{4}$$
$$\frac{7}{25}$$

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