Expressing multiplicative relationships as ratios and fractions | Maths

Starter quiz

If two things are proportional then the ratio of part to whole is maintained and the __________ relationship between parts is also maintained.

subtractive

additive

multiplicative ✓

inverse

opposite
$The ratio table shows a recipe for a pizza topping sauce. Complete this statement: Pizza sauce <Math>\times</Math> <span class="blank">______</span> = Puree.$

The ratio table shows a recipe for a pizza topping sauce. Complete this statement: Pizza sauce $\times$ ______ = Puree.

'120' ✓
$The ratio table shows a recipe for a pizza topping sauce. Complete this statement: Garlic <Math>\times</Math> <span class="blank">______</span> = Puree.$

The ratio table shows a recipe for a pizza topping sauce. Complete this statement: Garlic $\times$ ______ = Puree.

'30' ✓
A bowl of fruit contains apples and bananas. For every 3 apples, there are 5 bananas. There are 15 apples in the bowl. There are ______ bananas in the bowl.

'25' ✓
A box of fruit contains apples and bananas. For every 3 apples, there are 5 bananas. There are 80 pieces of fruit in total. How many bananas are there? ______ bananas.

'50' ✓
Which are equivalent ratios to: "For every 3 circles there are 5 squares."

"For every 9 circles there are 14 squares."

"For every 9 circles there are 15 squares." ✓

"For every 36 circles there are 60 squares." ✓

"For every 1.5 circles there are 2.5 squares." ✓

"For every 1 circle there are 1.5 squares."

Exit quiz

Which are equivalent to this ratio?

For every 1 t-shirt, there is 1 pair of shorts. ✓

For every 1 t-shirt, there are 2 pairs of shorts.

Number of pairs of shorts × 1 = Number of t-shirts ✓

Number of pairs of shorts × 0.5 = Number of t-shirts
Which are equivalent to this ratio?

For every cat, there are 4 mice. ✓

For every 2 cats, there are 9 mice.

For every 2 cats, there are 8 mice. ✓

Number of cats × 4 = Number of mice ✓

Number of cats × 5 = Number of mice
Which are equivalent to this ratio?

For every 4 phones, there are 3 houses.

For every 4 houses, there are 3 phones. ✓

Number of houses $\times \frac{3}{4}=$ Number of phones ✓

Number of phones $\times \frac{3}{4}=$ Number of houses

Number of phones $\times \frac{4}{3}=$ Number of houses ✓
A quantity is divided into two parts: A and B. Match each ratio with the correct fraction.

For every 2 As, there are 3 Bs

⇔

Fraction of A is $\frac{2}{5}$ ✓

For every 2 As, there are 5 Bs

⇔

Fraction of A is $\frac{2}{7}$ ✓

For every 2 As, there are 2 Bs

⇔

Fraction of A is $\frac{1}{2}$ ✓

For every 1 As, there are 2 Bs

⇔

Fraction of A is $\frac{1}{3}$ ✓
A quantity is divided into two parts: A and B. Match each ratio with the correct formula.

For every 2 As, there are 3 Bs.

⇔

A $\times\frac{3}{2}$ = B ✓

For every 2 As, there are 5 Bs.

⇔

A $\times\frac{5}{2}$ = B ✓

For every 2 As, there are 2 Bs.

⇔

A $\times1$ = B ✓

For every 1 As, there are 2 Bs.

⇔

A $\times2$ = B ✓
A quantity is divided into two parts: A and B. Match each fraction with the correct formula to find B.

A is $\frac{2}{3}$

⇔

A $\times\frac{1}{2}$ = B ✓

A is $\frac{3}{5}$

⇔

A $\times\frac{2}{3}$ = B ✓

A is $\frac{4}{7}$

⇔

A $\times\frac{3}{4}$ = B ✓

A is $\frac{1}{3}$

⇔

A $\times 2$ = B ✓

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Lesson Details

Key learning points

By expressing the multiplicative relationship as a ratio, it can be easier to scale further.
The relationship can be represented using a bar model.
A bar model shows both parts of the ratio as well as the whole.
A multiplicative relationship can be expressed as a fraction.
There are many different ways to express the relationship.

Common misconception

Pupils see the bar model and/or fraction as the whole as opposed to the proportion of the whole.

Emphasise equivalent fractions and equivalent bar models which show different parts to whole, but are the same proportion. e.g 3/5 = 60/100

Keywords

Proportionality - means when variables are in proportion if they have a constant multiplicative relationship.
Ratio - shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.
Fraction - shows us how many equal parts in a whole.