Year 9 Maths The Thai Guy

Lesson 11.1 · 25 min

Solving Ratio Problems

Sharing a quantity in a ratio, working from one share, and working from the difference between shares.

In this lesson you will learn to…

  • Simplify a ratio, including one with different units
  • Share a quantity in a given ratio
  • Find the other shares when you know one of them
  • Solve a problem when you are told the difference between two shares

Why this matters

Ratios are everywhere: recipes, mixing paint and concrete, splitting a bill, scale models and maps. The same short method answers all of them.

Simplifying first

Divide every part by the highest common factor: 24:40=3:524 : 40 = 3 : 5. If the quantities have different units, make the units the same before simplifying:

22 kg:1500 g=22 000:1500=44:322\ \text{kg} : 1500\ \text{g} = 22\,000 : 1500 = 44 : 3

Jadee’s mistake

For “Kamil and Sean share in the ratio 3:53 : 5, Sean gets 56 dollars more”, Jadee divided 56 by 3+5=83 + 5 = 8. But 56 is not the total — it is the difference, which is 5−3=25 - 3 = 2 parts. One part is 56÷2=2856 \div 2 = 28, not 7.

Always check. Add the shares to get the total, or subtract them to get the difference — whichever the question gave you.

Key rules and formulas

  • Find one part first

    Almost every ratio problem comes down to one question: what is one part worth? Once you know that, multiply by the number of parts you need.

  • Sharing a total

    350 dollars in the ratio is per part, giving , and .

  • Knowing one share

    If 130 children are the "10" in , one part is , so the "3" is .

  • Knowing the difference

    In the first share is parts bigger. If that difference is 21 dollars, one part is dollars.

Worked examples

Worked example 1

Sharing in a three-part ratio

Share 350 dollars between Emily, Samirah and Lola in the ratio .

Try it yourself first, then reveal the solution one step at a time.

Worked example 2

Change units first

Share 0.45 kg in the ratio .

Try it yourself first, then reveal the solution one step at a time.

Worked example 3

Using a difference

Kamil and Sean share money in the ratio . Sean gets 56 dollars more than Kamil. How much does each get?

Try it yourself first, then reveal the solution one step at a time.

Practice: ratio problems

10 questions

Ten questions. Find the value of one part first every time.
  1. Question 1 of 10Quick-fire drill
    Quick-fire: simplify each ratio. Type it like 3:5.

    8 questions · 60 seconds · answer as many as you can.

  2. Question 2 of 10Complete the tableFoundation
    Share each amount in the ratio given.
    AmountRatioFirst shareSecond share
    405 cm7 : 8
    0.24 kg (in g)3 : 5
    0.8 m (in cm)2 : 3
  3. Question 3 of 10Type the answer
    Divide 1 hour in the ratio . How many minutes is the larger share?
    minutes
  4. Question 4 of 10Fill the gaps
    The angles of a triangle are in the ratio . Find them.

    ° , ° , °

  5. Question 5 of 10Type the answer
    130 children voted for the zoo. The ratio of zoo to museum votes was . How many voted for the museum?
  6. Question 6 of 10Step by step
    Use the difference.
    Guntur and Eva share money in the ratio . Guntur gets 21 dollars more than Eva.
    1. How many more parts does Guntur have?

  7. Question 7 of 10Multiple choice
    Kamil and Sean share in the ratio ; Sean gets 56 dollars more. Jadee divided 56 by 8. What was her mistake?
  8. Question 8 of 10Type the answer
    A recipe mixes flour, margarine and butter in the ratio . If 400 g of margarine is used, what is the total mass?
    g
  9. Question 9 of 10Fill the gaps
    Two numbers are in the ratio and add up to 169. Find them.

    and

  10. Question 10 of 10Type the answerChallenge
    Votes for peach, orange and mango were in the ratio . 153 students chose orange. How many voted altogether?