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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
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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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Share activities with pupils
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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.

Keywords

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

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.

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).

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

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