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Oak National Academy
Oak National Academy
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New
New
Year 7

Dividing a whole number by a fraction

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

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New
New
Year 7

Dividing a whole number by a fraction

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

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. A diagram can help to show the underlying structure.
  2. The whole number can be split into a number of equal parts equal to the denominator.
  3. The numerator states how many equal parts are wanted.
  4. The value of each part is multiplied by the numerator.

Common misconception

Using the unitising method with a remainder, the remainder is not written as a fraction of the unit.

Drawing bar models, ensure that the unit is subdivided so the remainder can be seen as a fraction of the unit.

Keywords

  • Proper fraction - A proper fraction is a fraction where the numerator is less than the denominator

Pupils can use MWB or go to the board and draw bar models to show each step of dividing a whole number by a fraction. This should be completed in steps and each step should be checked; bar models are drawn, sub dividing and correct units used.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Video

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Starter quiz

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6 Questions

Q1.
How many halves are in 3 wholes? (You can use a bar model if it helps.)
3
Correct answer: 6
1.5
0
Q2.
How many quarters are in 5?
4
5
10
Correct answer: 20
25
Q3.
The bar model shows that there are lots of a $${1} \over {3}$$ in 4.
An image in a quiz
Correct Answer: 12
Q4.
The bar model shows that there are lots of a $${1} \over {5}$$ in 3.
An image in a quiz
Correct Answer: 15
Q5.
The Oak teacher gave 4 pupils a question, "How many tenths are there in 5?" Select the correct answer and explanation.
Laura says "There are 500 tenths because $$ 5\times 100$$ = 500"
Correct answer: Andeep says "There are 50 tenths because $$ 5\times 10$$ = 50"
Jun says "There are 50 tenths because each 10 wholes has five fifths."
Alex says "There are 2 tenths because $$ 10\div5 $$ = 2"
Q6.
Sort the following from largest to smallest.
1 - $$ 10\div \frac{1}{3}$$
2 - $$ 2\div \frac{1}{9}$$
3 - $$ 1\div \frac{1}{11}$$
4 - $$ 1\div \frac{1}{3}$$
5 - $$ 1\div \frac{1}{2}$$

Exit quiz

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6 Questions

Q1.
Using the bar model, work out $$ 4\div \frac{2}{3} = $$ .
An image in a quiz
Correct Answer: 6, six
Q2.
Using the bar model, work out $$ 3\div \frac{3}{4} = $$ .
An image in a quiz
Correct Answer: 4, four
Q3.
What does this bar model represent?
An image in a quiz
$$4 \div \frac{2}{3}$$
$$4 \div \frac{2}{7}$$
Correct answer: $$4 \div \frac{2}{5}$$
$$4 \div \frac{5}{2}$$
$$4 \div \frac{3}{5}$$
Q4.
Match the question on the left with the calculation on the right.
Correct Answer:$$ 6\div \frac{2}{5}$$,$$\frac{30}{5} \div \frac{2}{5}$$

$$\frac{30}{5} \div \frac{2}{5}$$

Correct Answer:$$ 4\div \frac{2}{5}$$,$$\frac{20}{5} \div \frac{2}{5}$$

$$\frac{20}{5} \div \frac{2}{5}$$

Correct Answer:$$ 10\div \frac{2}{5}$$,$$\frac{50}{5} \div \frac{2}{5}$$

$$\frac{50}{5} \div \frac{2}{5}$$

Correct Answer:$$ 5\div \frac{2}{5}$$,$$\frac{25}{5} \div \frac{2}{5}$$

$$\frac{25}{5} \div \frac{2}{5}$$

Q5.
What does this bar model represent?
An image in a quiz
$$4 \div \frac{2}{3}$$
$$4 \div \frac{3}{2}$$
Correct answer: $$4 \div \frac{3}{5}$$
$$6 \div \frac{3}{5}$$
Q6.
By drawing your own bar models or otherwise, match the calculations on the left with the answers on the right.
Correct Answer:$$4 \div \frac{3}{5}$$,$$6 {{2} \over {3}}$$

$$6 {{2} \over {3}}$$

Correct Answer:$$5 \div \frac{2}{3}$$,$$7{{1} \over {2}}$$

$$7{{1} \over {2}}$$

Correct Answer:$$2 \div \frac{3}{5}$$,$$3 {{1} \over {3}}$$

$$3 {{1} \over {3}}$$

Correct Answer:$$1 \div \frac{2}{3}$$,$$1 {{1} \over {2}}$$

$$1 {{1} \over {2}}$$