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Year 7

Deepening understanding of multiplication with fractions

I can generalise and fluently use strategies to multiply with mixed numbers.

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New
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Year 7

Deepening understanding of multiplication with fractions

I can generalise and fluently use strategies to multiply with mixed numbers.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. Mixed numbers can be converted into improper fractions.
  2. It is not necessary to convert both fractions.
  3. Each fraction should be considered to decide the most efficient way to convert.

Keywords

  • Product - A product is the result of two or more numbers multiplied together.

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

  • Improper fraction - An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

  • Mixed number - A mixed number is an improper fraction written as its integer part plus the fractional part where the fractional part is a proper fraction.

Common misconception

Only finding the product of the integers and fractional parts when multiplying mixed numbers.

Link back to the area model, there will be 2 parts which they have not found the area of.

Pupils will need to be confident with converting between improper fractions and mixed numbers. As the pupils are coming into the room have a mixed number written on the board and ask them to write down as many equivalent fractions as they can.
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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.
A number that has exactly 2 factors is a number.
Correct Answer: prime
Q2.
Which of the following will be less than 20?
Correct answer: $${2}\over{5}$$ $$\times20$$
$${20}\times1 {{1} \over {3}}$$
$${6}\over{5}$$ $$\times20$$
Correct answer: $${20}\times{19\over20}$$
Q3.
$${2}\over{3}$$ × $${1}\over{8}$$is than $${2}\over{3}$$ × $${1}\over{9}$$.
Correct Answer: greater, more, larger
Q4.
Using this fact, $${8}\over{85}$$ × $${25}\over{140}$$ = $${100}\over{5950}$$, which of the following are true?
$${2}\over{85}$$ × $${25}\over{140}$$ = $${20}\over{5950}$$
Correct answer: $${4}\over{85}$$ × $${25}\over{140}$$ = $${50}\over{5950}$$
Correct answer: $${16}\over{85}$$ × $${25}\over{140}$$ = $${200}\over{5950}$$
Correct answer: $${20}\over{85}$$ × $${25}\over{140}$$ = $${250}\over{5950}$$
Q5.
Calculate $${2}\over{3}$$ × $${3}\over{4}$$ × 15. Give your answer as a mixed number.
$${15}\over{2}$$
$${90}\over{12}$$
$$6 {{1} \over {2}}$$
Correct answer: $$7 {{1} \over {2}}$$
Q6.
Calculate $${132}\over{385}$$ × $${15}\over{18}$$ by writing each numerator and denominator as a product of its prime factors.
Correct answer: $${2}\over{7}$$
$${3}\over{7}$$
$${5}\over{7}$$
$${6}\over{7}$$

Exit quiz

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6 Questions

Q1.
Which of the following is the correct definition for an improper fraction?
A fraction where the numerator is greater than the denominator.
A fraction where the denominator is greater than the numerator.
Correct answer: A fraction where the numerator is greater than or equal to the denominator.
A fraction where the denominator is greater than or equal to the numerator.
Q2.
Convert $$3 {{1} \over {3}}$$ into an improper fraction.
$${7}\over{3}$$
$${8}\over{3}$$
$${9}\over{3}$$
Correct answer: $${10}\over{3}$$
Q3.
Calculate $$3 {{1} \over {3}}$$ × 13.
Correct answer: $$43 {{1} \over {3}}$$
$$43 {{2} \over {3}}$$
$$44 {{1} \over {3}}$$
$$44 {{2} \over {3}}$$
Q4.
Which of the following is not a correct method for calculating $$1 {{2} \over {5}}$$ × $$4 {{3} \over {4}}$$?
$${7}\over{5}$$ × $${19}\over{4}$$
Correct answer: 1 × 2 + $${2}\over{5}$$ × $${3}\over{4}$$
Q5.
Calculate $$2 {{3} \over {5}}$$ × $$3 {{2} \over {3}}$$.
$$8 {{8} \over {15}}$$
$$8 {{9} \over {15}}$$
$$9 {{7} \over {15}}$$
Correct answer: $$9 {{8} \over {15}}$$
$$9 {{9} \over {15}}$$
Q6.
Use the most efficient method to calculate $$5 {{1} \over {4}}$$ × $$1 {{3} \over {7}}$$. Give your answer in its simplest form.
$${15}\over{2}$$
$${17}\over{2}$$
Correct answer: $$7 {{1} \over {2}}$$
$$8 {{1} \over {2}}$$