The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1.

Checking and securing finding a fraction of a given amount

Maths

The multiplicative relationship is extended in the future unit by considering percentages and the connections between multiplicative relationships and direct proportion. By building on a secure understanding of fractions and ratio, pupils can see their understanding of multiplicative relationships being extended.

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

Understanding multiplicative relationships: fractions and ratio

Which of the following is not the reciprocal of 4?

Use a bar model to calculate $$3\over8$$ of 48

Which of the following are equivalent calculations for $$5\over9$$ of 72?

Calculate $$2 {{3} \over {5}}$$ × $$2\over7$$

What symbol separates the parts of a ratio?  E.g. the mathematical notation for writing 4 to 5.

Alex "60 triangles, so there are 20 squares because of the ratio is 3 : 1"

Laura "180 triangles, so there are 40 squares because of the ratio is 3 : 1"

Andeep "20 triangles, so there are 40 squares because of the ratio is 4 : 1"

Sofia "45 triangles, so there are 15 squares because of the ratio is 4 : 1"

Jun "34 triangles, so there are 26 squares because of the ratio is 4 : 1"

In a bag there are only triangles and squares. The ratio of triangles to squares is 3 : 1. There are 60 shapes in total. Who correctly worked out the number of squares?

Chocolates in a box either have red or blue wrappers.  The ratio of red to blue is 5 : 4. If the difference between the red and blue chocolates is 3, how many chocolates are in the box?

Chocolates in a box either have red or blue wrappers.  The ratio of red to blue is 3 : 2. Andeep eats 2 blue chocolates and now the ratio is 12 : 7. How many blues were in the box originally?

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