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

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

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

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

Deepening understanding of multiplication with fractions

Maths

In this unit, pupils generalised and developed their fluency of multiplying with fractions. In the future unit, this understanding is extended to ratio and connections between ratios and fractions are explored.

In the prior unit, pupils explored the structure of fractions and their relationship with decimals and integers. In this unit, pupils deepen their understanding of the arithmetic procedures involving fractions and integers.

Arithmetic procedures with fractions

A fraction where the numerator is greater than the denominator.

A fraction where the denominator is greater than the numerator.

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.

Which of the following is the correct definition for an improper fraction?

Convert $$3 {{1} \over {3}}$$ into an improper fraction.

1 × 2 + $${2}\over{5}$$ × $${3}\over{4}$$

Which of the following is not a correct method for calculating $$1 {{2} \over {5}}$$ × $$4 {{3} \over {4}}$$?

Calculate $$2 {{3} \over {5}}$$ × $$3 {{2} \over {3}}$$.

Use the most efficient method to calculate $$5 {{1} \over {4}}$$ × $$1 {{3} \over {7}}$$.  Give your answer in its simplest form.

A number that has exactly 2 factors is a {{ }} number.

Which of the following will be less than 20?

$${2}\over{3}$$ × $${1}\over{8}$$is {{ }} than $${2}\over{3}$$ × $${1}\over{9}$$.

$${2}\over{85}$$ × $${25}\over{140}$$ = $${20}\over{5950}$$

$${4}\over{85}$$ ×  $${25}\over{140}$$ = $${50}\over{5950}$$

$${16}\over{85}$$ × $${25}\over{140}$$ = $${200}\over{5950}$$

$${20}\over{85}$$ × $${25}\over{140}$$ = $${250}\over{5950}$$

Using this fact, $${8}\over{85}$$ × $${25}\over{140}$$ = $${100}\over{5950}$$, which of the following are true?

Calculate $${2}\over{3}$$ × $${3}\over{4}$$ × 15.  Give your answer as a mixed number.

Calculate $${132}\over{385}$$ × $${15}\over{18}$$ by writing each numerator and denominator as a product of its prime factors.

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