Dividing an amount in a ratio | Year 7

01 / LEARN

The idea, step by step

Count parts before finding amounts

To share a total in the ratio $2 : 3$ , imagine two equal-size parts for the first share and three for the second. The whole has five parts. Divide the total by five to find one part, then multiply that amount by two and by three. Equal-size parts do not mean equal final shares.

Check both conditions

Correct shares add to the original total and simplify to the requested ratio in the stated order. Include units. For an indivisible collection, think about whether fractional shares make sense. When one share is given instead of the total, use the matching ratio entry to find a part; do not divide by the sum automatically.

A common trap

Dividing the total by each ratio entry separately.

Instead: For a given total, divide by the sum of the entries to find a single part. Each entry then tells you how many parts that share receives.

02 / WORKED EXAMPLES

See the thinking

Example 1

Share money

Share 40 dollars between Ali and Bea in the ratio $3 : 5$ .

There are $3 + 5 = 8$ parts.
One part is $40 / 8 = 5$ dollars.
Ali gets $3 (5) = 15$ dollars; Bea gets $5 (5) = 25$ dollars.
Check $15 + 25 = 40$ and $15 : 25 = 3 : 5$ .

Ali 15 dollars; Bea 25 dollars.

Example 2

Share a collection three ways

Share 60 counters in the ratio $2 : 3 : 5$ .

There are $2 + 3 + 5 = 10$ parts.
One part is $60 / 10 = 6$ counters.
Multiply 6 by 2, 3 and 5.

12, 18 and 30 counters.

Check your understanding

Share 24 stickers in the ratio $1 : 3$ .

Show answer

6 stickers and 18 stickers.

Four parts make 24, so one part is 6. The second share has three parts.

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Share 30 beads in the ratio $2 : 3$ .
2 marks
Share 56 dollars in the ratio $3 : 5$ .
2 marks
Split 45 L of juice into orange:apple in the ratio $4 : 5$ .
2 marks
Divide 72 m of ribbon into lengths in the ratio $1 : 2 : 3$ .
2 marks
A team shares 48 points in the ratio $5 : 3$ . Sam is given 30 and Jo 18. Check both conditions.
3 marks
Two boxes contain pencils in the ratio $2 : 5$ . The larger box holds 35 pencils. Find the number in both boxes.
3 marks

Read the worked solutions

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

Share 30 beads in the ratio $2 : 3$ .
2 marks
Five parts make 30; one part is 6.
Multiply 6 by 2 and by 3.
12 beads and 18 beads.
Share 56 dollars in the ratio $3 : 5$ .
2 marks
Eight parts make 56 dollars; one part is 7 dollars.
Multiply 7 by 3 and by 5.
21 dollars and 35 dollars.
Split 45 L of juice into orange:apple in the ratio $4 : 5$ .
2 marks
Nine parts make 45 L; one part is 5 L.
The shares are $4 (5) = 20$ and $5 (5) = 25$ L.
20 L orange and 25 L apple.
Divide 72 m of ribbon into lengths in the ratio $1 : 2 : 3$ .
2 marks
Six parts make 72 m, so one part is 12 m.
Multiply 12 by each entry.
12 m, 24 m and 36 m.
A team shares 48 points in the ratio $5 : 3$ . Sam is given 30 and Jo 18. Check both conditions.
3 marks
$30 + 18 = 48$ .
Dividing $30 : 18$ by 6 gives $5 : 3$ .
The shares are correct.
Two boxes contain pencils in the ratio $2 : 5$ . The larger box holds 35 pencils. Find the number in both boxes.
3 marks
Five parts are 35, so one part is 7.
The smaller box has $2 (7) = 14$ .
The total is $14 + 35 = 49$ .
49 pencils.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Year 7 ratio comparisons and practical proportional models, including units, part-to-whole meaning and assumptions.

Official curriculum source ↗

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