Year 9 maths lesson · Rates and Ratios

Ratio Problems

Solve ratio problems where you work backwards from one share, find the total from one share, and use the difference between shares to find each amount.

  • About 3–6 minutes
  • 5 quick questions as you go
  • Then about 5 minutes of practice
Practice questions → Set for Class

Worked examples

Ratio 2 : 3, Bob gets 12 oranges. How many does Alice get?

  1. Bob’s 3 parts = 12
  2. 1 part = 12 ÷ 3 = 4
  3. Alice = 2 × 4 = 8 oranges

Ratio 3 : 2, Alice gets 9 candies. What’s the total?

  1. 3 parts = 9 → 1 part = 3
  2. Bob = 2 × 3 = 6
  3. Total = 9 + 6 = 15 candies

Ratio 3 : 5, first person gets $24. What’s the total?

  1. 3 parts = $24 → 1 part = $8
  2. Second = 5 × $8 = $40
  3. Total = $24 + $40 = $64

Ratio 4 : 7, difference between shares is $15. How much does each get?

  1. Difference in parts = 7 − 4 = 3
  2. 3 parts = $15 → 1 part = $5
  3. First = 4 × $5 = $20, Second = 7 × $5 = $35
  4. Check: $35 − $20 = $15 ✓

Before this lesson

It helps to be comfortable with:

Lesson transcript

Everything the lesson says, word for word

If Alice and Bob share oranges in the ratio 2 to 3 and Bob gets 12 oranges, how many does Alice get? Bob’s share is 3 parts. 3 parts equals 12. So dividing these 12 oranges into 3 equal groups, we get 4. So one part is 4 oranges. Alice gets 2 parts — that’s 2 times 4, which is 8 oranges.

If Alice and Bob share candies in the ratio 3 to 2 and Alice gets 9 candies, what’s the total number of candies? Alice’s share is 3 parts. 3 parts equals 9. So dividing these 9 candies into 3 equal groups, we get 3. So one part is 3 candies. Bob gets 2 parts — that’s 2 times 3, which is 6 candies. The total is 9 plus 6 — that’s 15 candies.

Now without a picture. Two people share money in the ratio 3 to 5. If the first person gets 24 dollars, what’s the total? 3 parts equals 24. So each part is 24 divided by 3, which is 8 dollars. The first person gets 3 times 8 — that’s 24 dollars. The second person gets 5 times 8 — that’s 40 dollars. 24 plus 40 equals 64. The total is 64 dollars.

Now let’s try a different type. What if you know the difference between two shares?

Two people share pocket money in the ratio 4 to 7. The difference between their shares is 15 dollars. How much does each person get? The difference in parts is 7 minus 4, which is 3 parts. 3 parts equals 15 dollars. So one part is 15 divided by 3, which is 5 dollars. The first person gets 4 times 5 — that’s 20 dollars. The second person gets 7 times 5 — that’s 35 dollars. Quick check: 35 minus 20 equals 15. Perfect.

More Rates and Ratios lessons

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