Ratio scaling and division review | Year 8

01 / LEARN

The idea, step by step

A ratio compares matching quantities

In the ratio $2 : 3$ , the first quantity has two equal-sized parts and the second has three. Multiplying both terms by the same positive number changes the size of the quantities but preserves their relationship. Dividing both terms by a common factor simplifies the ratio.

Match units before comparing: $2$ m to $50$ cm means $200 : 50 = 4 : 1$ . Keeping unlike units without converting can describe a different comparison.

Find the size of one part

When a total is shared in the ratio $a : b$ , add the parts first. Divide the total by $a + b$ , then multiply that single-part amount by each term. Check that the shares add back to the total.

If one share is given instead of the total, divide by the number of parts in that share. Do not divide by the total parts until you actually know the combined amount.

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

A common trap

To share in the ratio $2 : 3$ , divide the total by 2 and by 3 separately.

Instead: Both shares use the same part size. Add $2 + 3$ first, then split the total into five equal parts.

02 / WORKED EXAMPLES

See the thinking

Example 1

Share a total

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

There are $2 + 3 = 5$ equal parts.
Each part is $25 \div 5 = 5$ L.
White is $2 \times 5 = 10$ L; blue is $3 \times 5 = 15$ L.
Check: $10 + 15 = 25$ L and $10 : 15 = 2 : 3$ .

10 L white and 15 L blue.

Example 2

One share is known

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

The three boy-parts represent 12, so one part is $12 \div 3 = 4$ .
The five girl-parts represent $5 \times 4 = 20$ .
The full club has $12 + 20 = 32$ members.

20 girls.

Check your understanding

Share 42 in the ratio $3 : 4$ .

Show answer

18 and 24.

Seven parts make 42, so each part is 6; the shares are $3 \times 6$ and $4 \times 6$ .

03 / WORKSHEET

Your turn

6 questions · 13 marks · Work at your own pace.

Worksheet PDF 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 ↗

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