Ratio scaling and division review | Year 8

01 / LEARN

Understand the idea.

A ratio compares matching quantities

A ratio compares quantities in a stated order. White:blue $= 2 : 3$ means two equal parts of white for every three parts of blue. An equivalent ratio multiplies or divides both terms by the same positive number, preserving that mixture.

First express matching kinds of quantity in the same unit. For $2$ m and $50$ cm, compare $200 : 50$ , which simplifies to $4 : 1$ . Comparing the unconverted numbers $2 : 50$ would give the wrong relationship.

Find the size of one part

To share a total, count all the ratio parts before dividing. In $a : b$ , the total contains $a + b$ equal parts. Find the amount in one part, then multiply it by each term to obtain the two shares.

If only one share is known, that amount represents just its own ratio parts. Divide by that term, then scale to the other share. Finally check both the order of the ratio and that the shares give the correct total.

one part = \frac{total amount}{a + b}

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Share a total

Share 25 L of paint in the ratio white:blue $= 2 : 3$ .

Worked solution

1
Count the parts in the complete mixture.
$2 + 3 = 5$
The total paint includes both the white parts and the blue parts.
2
Find the amount in one part.
$25 \div 5 = 5 L$
All five ratio parts have the same volume.
3
Scale to each colour.
$\begin{aligned} White & = 2 \times 5 = 10 L \\ Blue & = 3 \times 5 = 15 L \end{aligned}$
White uses two parts and blue uses three parts.
4
Check the total and the ratio.
$\begin{aligned} 10 + 15 & = 25 L \\ 10 : 15 & = 2 : 3 \end{aligned}$
Both the supplied volume and the requested mixture are recovered.

Answer

10 L white and 15 L blue.

EXAMPLE 02

One share is known

A club has boys:girls $= 3 : 5$ . There are 12 boys. How many girls are there?

Worked solution

1
Match the known share to its ratio term.
$3 parts = 12 boys$
The first term in boys:girls describes boys, not all club members.
2
Find the number represented by one part.
$12 \div 3 = 4$
The twelve boys occupy three equal ratio parts.
3
Find and check the girls share.
$\begin{aligned} Girls & = 5 \times 4 = 20 \\ 12 : 20 & = 3 : 5 \end{aligned}$
Five parts are required for girls, and the completed ratio simplifies correctly.

Answer

20 girls.

03 / YOUR TURN

Try it yourself.

Check your understanding

Share 42 in the ratio $3 : 4$ .

Show answer & reasoning

18 and 24.

There are $3 + 4 = 7$ parts, so each part is $42 \div 7 = 6$ . The shares are $3 \times 6 = 18$ and $4 \times 6 = 24$ ; their sum is $42$ and their ratio simplifies to $3 : 4$ .

Keep practising

6 worksheet questions · 13 marks

Open worksheet Worked solutions

Read the questions online

Simplify $18 : 30$ .
1 mark
Write the ratio 2 m to 50 cm in simplest form.
2 marks
Complete the equivalent ratio $4 : 7 = 20 : □$ .
2 marks
Share AUD 96 in the ratio $5 : 3$ .
3 marks
A:B $= 2 : 5$ . B is 35. Find A and the total.
3 marks
Juice:water $= 3 : 4$ . A drink contains 750 mL of juice. How much water is needed?
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Simplify $18 : 30$ .
1 mark
Divide both terms by their common factor 6.
$3 : 5$ .
Write the ratio 2 m to 50 cm in simplest form.
2 marks
Convert 2 m to 200 cm.
$200 : 50 = 4 : 1$ .
$4 : 1$ .
Complete the equivalent ratio $4 : 7 = 20 : □$ .
2 marks
The first term was multiplied by 5.
Multiply the second term by 5: $7 \times 5 = 35$ .
35.
Share AUD 96 in the ratio $5 : 3$ .
3 marks
Total parts: $5 + 3 = 8$ .
One part is $96 \div 8 = 12$ .
Shares are $5 \times 12 = 60$ and $3 \times 12 = 36$ .
AUD 60 and AUD 36.
A:B $= 2 : 5$ . B is 35. Find A and the total.
3 marks
One part is $35 \div 5 = 7$ .
A is $2 \times 7 = 14$ .
The total is $14 + 35 = 49$ .
A is 14; the total is 49.
Juice:water $= 3 : 4$ . A drink contains 750 mL of juice. How much water is needed?
2 marks
One part is $750 \div 3 = 250$ mL.
Four parts are $4 \times 250 = 1, 000$ mL.
1,000 mL of water.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Ratio scaling and division review; unit rates; comparing rates and best buys; speed, distance and time; converting compatible units; direct-proportion tables and graphs; modelling practical rate problems and checking assumptions.

Official curriculum source ↗

In this lesson

Understand the idea.

A ratio compares matching quantities

Find the size of one part

See the method in action.

Share a total

Count the parts in the complete mixture.

Find the amount in one part.

Scale to each colour.

Check the total and the ratio.

One share is known

Match the known share to its ratio term.

Find the number represented by one part.

Find and check the girls share.

Try it yourself.

Check your understanding

Keep practising