Understand the idea.
Count parts before finding amounts
To divide a total in a ratio, imagine equal-size parts. A ratio of assigns two parts to the first share and three to the second. The total therefore contains five equal parts; divide it by to find one part.
Multiply the value of one part by each ratio entry. The parts are equal, but the final shares need not be. Keep the names in the stated order so the larger share reaches the intended person or group.
Check both conditions
Check two conditions: the shares must add to the original total and must have the requested ratio. Either check alone is insufficient. Two amounts might add correctly while being shared equally instead of in the required proportion.
Distinguish a given total from a given individual share. If one share is known, divide it by its matching ratio entry to find one part. For indivisible objects, also check that the calculated shares are whole numbers.
See the method in action.
Share money
Share 40 dollars between Ali and Bea in the ratio .
Worked solution
- 1
Count the equal parts.
Ali’s three parts and Bea’s five parts together represent all forty dollars.
- 2
Find the value of one part.
The total is divided equally among the eight ratio parts.
- 3
Build each person's share.
Multiply the same part value by the number of parts assigned to each person.
- 4
Check the total and the ratio.
Both the entire amount and the requested relative shares are preserved.
Ali 15 dollars; Bea 25 dollars.
Share a collection three ways
Share 60 counters in the ratio .
Worked solution
- 1
Count all three groups' parts.
The total is represented by the sum of every ratio entry.
- 2
Find one equal part.
Sixty counters are shared among ten equal-size parts.
- 3
Calculate the three shares.
Each entry counts how many six-counter parts its group receives.
- 4
Check the completed sharing.
All counters are used, and dividing the shares by six recovers the given ratio.
12, 18 and 30 counters.
Try it yourself.
Check your understanding
Share 24 stickers in the ratio .
Show answer & reasoning
6 stickers and 18 stickers.
The ratio has equal parts, so each is stickers. The shares are and stickers; together they make .
Keep practising
6 worksheet questions · 14 marks
Read the questions online
- Share 30 beads in the ratio .2 marks
- Share 56 dollars in the ratio .2 marks
- Split 45 L of juice into orange:apple in the ratio .2 marks
- Divide 72 m of ribbon into lengths in the ratio .2 marks
- A team shares 48 points in the ratio . Sam is given 30 and Jo 18. Check both conditions.3 marks
- Two boxes contain pencils in the ratio . 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 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 .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 .2 marks
Nine parts make 45 L; one part is 5 L.
The shares are and L.
20 L orange and 25 L apple. - Divide 72 m of ribbon into lengths in the ratio .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 . Sam is given 30 and Jo 18. Check both conditions.3 marks
.
Dividing by 6 gives .
The shares are correct. - Two boxes contain pencils in the ratio . 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 .
The total is .
49 pencils.
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 ↗