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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 8 of 10

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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

A diagram can help to show the underlying structure.
Another method is the use the reciprocal of the dividing fraction.
The reciprocal is the multiplicative inverse.
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?"

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).

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Prior knowledge 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?

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

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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

-1

itself

Q2.
Match the value on the left with its reciprocal on the right.

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

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

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

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

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

$$\frac{5}{16}$$

$$\frac{15}{48}$$

$$\frac{20}{9}$$

Correct answer: $$\frac{9}{20}$$

Q6.
Work out the missing length given the area.

$$\frac{7}{8}$$

$$\frac{4}{7}$$

Correct answer: $$\frac{7}{4}$$

$$\frac{7}{25}$$

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UnitMaths / Arithmetic procedures with fractions

Maths

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Dividing a fraction by a fraction

Dividing a fraction by a fraction

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Using a bar model or otherwise, complete the statement $$ 6\div \frac{2}{5}$$ = .

Q2.Using a bar model or otherwise, complete the statement $$ 10\div \frac{2}{3}$$ = .

Q3.Without using a bar model, which calculation is the most efficient calculation to work out $$ 8\div \frac{2}{5}$$ ?

Q4.Using a model or otherwise, work out the answer for $$5 \div \frac{2}{7}$$.

Q5.Here is a bar model. Three of the Oak students think they know what the question was. Which student is correct?

Q6.Order the following from largest to smallest. Drawing bar models to find the mixed number may help.

Assessment exit quiz

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 __________

Q2.Match the value on the left with its reciprocal on the right.

Q3.Which of the following is the answer to $$\frac{3}{4} \div \frac{2}{5}$$?

Q4.Which of the following is the answer to $$\frac{2}{5} \div \frac{3}{7}$$?

Q5.Work out the missing length given the area.

Q6.Work out the missing length given the area.

Lesson appears in

UnitMaths / Arithmetic procedures with fractions

Maths

Q1.
Using a bar model or otherwise, complete the statement $$ 6\div \frac{2}{5}$$ = .

Q2.
Using a bar model or otherwise, complete the statement $$ 10\div \frac{2}{3}$$ = .

Q3.
Without using a bar model, which calculation is the most efficient calculation to work out $$ 8\div \frac{2}{5}$$ ?

Q4.
Using a model or otherwise, work out the answer for $$5 \div \frac{2}{7}$$.

Q5.
Here is a bar model. Three of the Oak students think they know what the question was. Which student is correct?

Q6.
Order the following from largest to smallest. Drawing bar models to find the mixed number may help.

Q1.
A reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to __________

Q2.
Match the value on the left with its reciprocal on the right.

Q3.
Which of the following is the answer to $$\frac{3}{4} \div \frac{2}{5}$$?

Q4.
Which of the following is the answer to $$\frac{2}{5} \div \frac{3}{7}$$?

Q5.
Work out the missing length given the area.

Q6.
Work out the missing length given the area.