A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.

Multiplicative relationships in context

Maths

Checking understanding of multiplicative relationships

Securing understanding of ratio as a multiplicative relationship

Expressing multiplicative relationships as ratios and fractions

Multiplicative relationships

Equivalent multiplicative relationships

Representing a multiplicative relationship

Ratio language and notation

Checking and securing finding a fraction of a given amount

Deepening understanding with fractions of a given amount

Expressing one number as a fraction of another

Dividing a quantity into a given ratio

Determining the whole

Determining the part

Describing exchange rates with ratio

Describing more conversions with ratio

Problem solving with fractions and ratios

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.

This unit introduces the concept of multiplicative relationsihps, and connects fractions to the idea of ratios. Ratios are then explored in depth and used to solve contextual problems such as those involving exchange rates and general conversions.

Understanding multiplicative relationships: fractions and ratio

This multiplicative relationship applies to lots of real life contexts. Select which of the following show real life use of ratio.

For every £2, you get $3. This means for every £1, you receive ${{}}. 

To make vegetable soup, Jun needs 8 carrots, 4 potatoes, 200 ml water and 2 stock cubes. Jun has 23 carrots, 10 potatoes, 600 ml of water and 5 stock cubes. What must be added for the correct ratio?

Here is a ratio table showing the conversion from pounds (£) to USA dollars ($). Select the **incorrect** ratio.

Select the statements which are equivalent to "For every £1, you get €2.50"

Starting with the best exchange rate, put the exchange rates for converting £ to $ in order from best to worst. (I.e. the more dollars you get per pound is the best exchange rate.)

Number of smoothies × 8 = Slices of apple

Slices of apples ×  0.5 = Slices of banana

Slices of banana × 50 = Amount of yogurt

Here is a ratio table showing how to make a smoothie. Select which of the following multiplicative relationships show this ratio.

Here is a ratio table showing the ratio between eggs and sugar in a pudding. For every 2 parts eggs, there are 3 parts sugar in the pudding. Which of the rows is incorrect?

Work out how many slices of apple are needed to make 12 smoothies if 8 slices of apple are needed for 1 smoothie.

The ratio table can be used to make a cake. How many bananas are needed when 600 g of sugar is used?

The ratio table can be used to make some cakes. Sofia uses 15 eggs to make some cakes for the school fete. Sofia should use {{ }} g of flour.

The ratio table can be used to make some cakes. Andeep uses 1 kg of flour to make some cakes for the school fete. Andeep should use {{ }} eggs.

Starter Quiz

Here is a ratio table showing how to make a smoothie. Select which of the following multiplicative relationships show this ratio.