All 8 problems from "Sum & Ratio" with complete step-by-step worked solutions: recognising the type, the idea, the working steps and the conclusion. Use this page to review with your child after the animated lesson, or let them check their own working against it.
Two quantities are in the ratio 2:3. Their total is 25. What is the smaller quantity?
Key idea: Divide the total by the total number of parts to find one part.
A ratio of 2:3 with a total of 25 — a sum–ratio problem.
The total is split into 2 + 3 = 5 equal parts.
One part = 25 ÷ 5 = 5.
Smaller = 2 × 5 = 10.
So: So the smaller quantity is 10.
A and B share $30 in the ratio 1:2. How much does B get?
Key idea: One part first: total ÷ total parts, then multiply by each share.
$30 shared in the ratio 1:2 — the total splits into 3 parts.
Find one part, then B takes 2 of them.
One part = 30 ÷ (1 + 2) = $10.
B gets 2 × $10 = $20.
So: So B gets $20.
Two numbers are in the ratio 3:2 and add up to 40. What is the larger number?
Key idea: Divide the total by the total number of parts to find one part.
Ratio 3:2 adding to 40 — split the total into 5 parts.
One part, then the larger side takes 3 parts.
One part = 40 ÷ (3 + 2) = 8.
Larger = 3 × 8 = 24.
So: So the larger number is 24.
Red and blue beads are in the ratio 4:5. There are 63 beads in total. How many blue beads are there?
Key idea: Divide the total by the total number of parts to find one part.
Red and blue beads in the ratio 4:5, 63 beads in all.
63 beads split into 9 equal parts; blue takes 5.
One part = 63 ÷ (4 + 5) = 7.
Blue = 5 × 7 = 35.
So: So there are 35 blue beads.
Three children share 60 sweets in the ratio 2:3:5. The first child gets ___, the second gets ___, and the third gets ___.
Key idea: Three shares still start with one part: total ÷ total parts.
60 sweets shared 2:3:5 among three children.
The total splits into 2 + 3 + 5 = 10 parts.
One part = 60 ÷ 10 = 6.
Shares: 2 × 6 = 12, 3 × 6 = 18, 5 × 6 = 30.
So: So the children get 12, 18 and 30 sweets.
If the ratio of cats to dogs is 3:7 and there are 50 animals, how many cats are there?
Key idea: Divide the total by the total number of parts to find one part.
Cats to dogs is 3:7 with 50 animals altogether.
50 animals split into 10 parts; cats take 3.
One part = 50 ÷ (3 + 7) = 5.
Cats = 3 × 5 = 15.
So: So there are 15 cats.
A 72 cm ribbon is cut into pieces in the ratio 1:2:3. How long is the longest piece?
Key idea: One part first, then the longest piece takes the most parts.
A 72 cm ribbon cut in the ratio 1:2:3.
72 cm splits into 6 parts; the longest takes 3.
One part = 72 ÷ (1 + 2 + 3) = 12 cm.
Longest = 3 × 12 = 36 cm.
So: So the longest piece is 36 cm.
Mia and Sam earn money in the ratio 5:3. Together they earned $96. How much more did Mia earn than Sam?
Key idea: Find both shares first — the question asks for the gap between them.
Earnings in the ratio 5:3 totalling $96, but the DIFFERENCE between the shares is asked for.
One part gives both shares; subtract at the end.
One part = 96 ÷ (5 + 3) = $12.
Mia = 5 × 12 = $60 and Sam = 3 × 12 = $36.
Difference = 60 − 36 = $24.
So: So Mia earned $24 more than Sam.
Two quantities are in the ratio 3:2. Together they total 40. What is the value of each quantity?
Shortcuts: Space (play), Arrow keys (step), R (reset), F (fullscreen)
We have two quantities in a ratio of 3:2 with a combined sum of 40. The big question of this lesson: what is each quantity worth?
Do not rush to calculate — count the parts first.
Change the numbers and watch the diagram redraw itself:
