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Equivalent multiplicative relationships

I can appreciate that there are an infinite number of pairs of numbers for any given multiplicative relationship.

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Lesson 6 of 17

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Year 7

Equivalent multiplicative relationships

I can appreciate that there are an infinite number of pairs of numbers for any given multiplicative relationship.

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Lesson details

Key learning points

There is a multiplicative relationship between the ratio parts, and other equivalent ratios.
Ratios can be expressed as fractions.
There are infinitely many equivalent fractions.
There are infinitely many equivalent ratios.

Keywords

Proportionality - Proportionality means when variables are in proportion if they have a constant multiplicative relationship.

Common misconception

Using multiplication as repeated addition leads to incorrect additive strategies of ratios.

Focus on the multiplicative relationships between parts to whole or whole to parts. Ratio tables can help see this more easily.

Using gridded or squared paper, pupils can do some pixelated art with specific ratios. e.g For every 3 black, there must be 1 white. Start with a 5 x 5, then a 6 x 6. Emphasising the ratio

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Licence

This content is © Oak National Academy Limited (2026), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge starter quiz

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6 Questions

Q1.
Proportionality means when __________ are in proportion if they have a constant multiplicative relationship.

multiplicatives

Correct answer: variables

additives

constants

Q2.
Match the equivalent fractions.

Correct Answer:$$\frac{2}{3}$$,$$\frac{6}{9}$$

Correct Answer:$$\frac{3}{5}$$,$$\frac{9}{15}$$

Correct Answer:$$\frac{5}{7}$$,$$\frac{15}{21}$$

Correct Answer:$$\frac{1}{2}$$,$$\frac{3}{6}$$

Q3.
For every 2 apples, there are 5 bananas. If there are 10 apples, how many bananas are there?

Correct Answer: 25, twenty-five, twentyfive, twenty five

Q4.
For every 2 apples, there are 9 bananas. If there are 33 pieces of fruit in total, how many bananas are there?

Correct answer: 27

Q5.
Packs of fruit are in the ratio of 2 apples to 3 pears to 5 bananas. When there are 27 pears, how many apples and bananas are needs to make as many packs of fruit as possible?

12 apples and 20 bananas

19 apples and 29 bananas

Correct answer: 18 apples and 45 bananas

20 apples and 30 bananas

Q6.
Packs of fruit are in the ratio of 2 apples to 3 pears to 5 bananas. When there are 48 pears, how many apples and bananas are needs to make as many packs of fruit as possible?

18 apples and 23 bananas

33 apples and 83 bananas

Correct answer: 32 apples and 80 bananas

40 apples and 80 bananas

Assessment exit quiz

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6 Questions

Q1.
How many equivalent ratios are there to "For every 1 apple, there are 2 bananas."?

Correct answer: infinite

1000

Q2.
Select the equivalent ratios to "For every 10 stars, there are 2 moons."

Correct answer: For every 5 stars, there is 1 moon.

Correct answer: For every 20 stars, there are 4 moons.

Correct answer: For every 25 stars, there are 5 moons.

For every 2 stars, there are 0.1 moons.

For every 8 stars, there are 4 moons.

Q3.
What is the equivalent ratio for this?

For every 1 pair of shorts, there are 3 t-shirts.

Correct answer: For every 1 t-shirt, there are 3 pairs of shorts.

Correct answer: For every 5 t-shirts, there are 15 pairs of shorts.

For every 4 t-shirts, there are 5 pairs of shorts.

Q4.
What is the ratio of shaded to not shaded?

Correct answer: For every 9 shaded, there are 16 not shaded.

For every 3 shaded, there are 2 not shaded.

For every 2 shaded, there are 3 not shaded.

For every 1 shaded, there is 1 not shaded.

Q5.
What is the ratio of shaded to not shaded?

Correct answer: For every 10 shaded, there are 15 not shaded.

For every 2 shaded, there are 5 not shaded.

Correct answer: For every 2 shaded, there are 3 not shaded.

For every 3 shaded, there are 2 not shaded.

Q6.
Three pieces of wood are cut so that length of piece A × 3 = length of piece B, length of piece B × 2 = length of piece C. Find the length of piece C in cm if the total length of all 3 pieces is 65 cm

Correct Answer: 40, 40 cm, 40cm

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UnitMaths / Understanding multiplicative relationships: fractions and ratio

Maths

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Equivalent multiplicative relationships

Equivalent multiplicative relationships

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Proportionality means when __________ are in proportion if they have a constant multiplicative relationship.

Q2.Match the equivalent fractions.

Q3.For every 2 apples, there are 5 bananas. If there are 10 apples, how many bananas are there?

Q4.For every 2 apples, there are 9 bananas. If there are 33 pieces of fruit in total, how many bananas are there?

Q5.Packs of fruit are in the ratio of 2 apples to 3 pears to 5 bananas. When there are 27 pears, how many apples and bananas are needs to make as many packs of fruit as possible?

Q6.Packs of fruit are in the ratio of 2 apples to 3 pears to 5 bananas. When there are 48 pears, how many apples and bananas are needs to make as many packs of fruit as possible?

Assessment exit quiz

6 Questions

Q1.How many equivalent ratios are there to "For every 1 apple, there are 2 bananas."?

Q2.Select the equivalent ratios to "For every 10 stars, there are 2 moons."

Q3.What is the equivalent ratio for this?

Q4.What is the ratio of shaded to not shaded?

Q5.What is the ratio of shaded to not shaded?

Q6.Three pieces of wood are cut so that length of piece A × 3 = length of piece B, length of piece B × 2 = length of piece C. Find the length of piece C in cm if the total length of all 3 pieces is 65 cm

Lesson appears in

UnitMaths / Understanding multiplicative relationships: fractions and ratio

Maths

Q1.
Proportionality means when __________ are in proportion if they have a constant multiplicative relationship.

Q2.
Match the equivalent fractions.

Q3.
For every 2 apples, there are 5 bananas. If there are 10 apples, how many bananas are there?

Q4.
For every 2 apples, there are 9 bananas. If there are 33 pieces of fruit in total, how many bananas are there?

Q5.
Packs of fruit are in the ratio of 2 apples to 3 pears to 5 bananas. When there are 27 pears, how many apples and bananas are needs to make as many packs of fruit as possible?

Q6.
Packs of fruit are in the ratio of 2 apples to 3 pears to 5 bananas. When there are 48 pears, how many apples and bananas are needs to make as many packs of fruit as possible?

Q1.
How many equivalent ratios are there to "For every 1 apple, there are 2 bananas."?

Q2.
Select the equivalent ratios to "For every 10 stars, there are 2 moons."

Q3.
What is the equivalent ratio for this?

Q4.
What is the ratio of shaded to not shaded?

Q5.
What is the ratio of shaded to not shaded?

Q6.
Three pieces of wood are cut so that length of piece A × 3 = length of piece B, length of piece B × 2 = length of piece C. Find the length of piece C in cm if the total length of all 3 pieces is 65 cm