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

An operation is commutative if the values it is operating on can be written in either order without changing the calculation.

Prime factors are the factors of a number that are, themselves, prime.

Securing 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 prime number has exactly {{ }} factors.

Which of the following will be less than 8?

$${1}\over{7}$$ × $${1}\over{8}$$is {{ }} than $${1}\over{6}$$ × $${1}\over{8}$$.

$${4}\over{76}$$ × $${36}\over{150}$$ = $${72}\over{5700}$$

$${8}\over{76}$$ × $${18}\over{150}$$ = $${72}\over{5700}$$

$${16}\over{76}$$ × $${36}\over{150}$$ = $${288}\over{5700}$$

$${20}\over{76}$$ × $${36}\over{150}$$ = $${350}\over{5700}$$

Using this fact, $${8}\over{76}$$ × $${36}\over{150}$$ = $${144}\over{5700}$$, which of the following are true?

Calculate 25 × $${3}\over{5}$$ × $${5}\over{6}$$.  Give you answer as a mixed number.

Calculate $${28}\over{63}$$ × $${105}\over{1155}$$ by writing each numerator and denominator as a product of its prime factors.

What fraction of the rectangle is shaded?

What calculation is represented by the area of the rectangle shaded?

Calculate $${2}\over{3}$$ × $${4}\over{5}$$.

Calculate $${2}\over{3}$$ × $${3}\over{5}$$ × $${1}\over{4}$$.

Calculate $${3}\over{5}$$ × $${5}\over{9}$$ × $${3}\over{4}$$, give your answer in its simplest form.  Try to simplify before calculating.

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