DeepMaths Junior

Junior Maths Book 1 AI Learning System

For Years 7-9 - Numbers & Statistics

Chapter 3: Ratio, Proportion and Rates

Ratio, Proportion and Rates

See ratio as a relationship that can be scaled, compared and used to solve real problems.

Junior Maths Book 1 pages 33-508 minutes

AI teacher

Start the short explanation, then use the visual model and practice before returning to the workbook.

Voice: Browser voice

Workbook pages

Junior Maths Book 1 pages 33-50

Use ratio notation, sharing, scale, recipes, currency exchange, best buys, rates and multi-step applications.

AI explanation

The AI teacher builds ratios with bar models, double number lines and tables. Students learn to preserve the relationship while scaling quantities up or down.

  1. 1A ratio compares quantities in a fixed order.
  2. 2Simplifying a ratio keeps the relationship but uses smaller numbers.
  3. 3Sharing in a ratio starts by finding the value of one part.
  4. 4Rates compare quantities with different units, such as dollars per kilogram.

Animated teaching

See the method

A ratio bar splits into parts, then a proportion table scales recipes, currency and best-buy quantities.

A
A
A
B
B
B
B

Ratio 3 : 4 means 7 equal parts.

Parts
3
4
7
Value
$36
$48
$84
Unit
$12
$12
$12

Why this method works

  • Ratio works by multiplying or dividing every part by the same scale factor.
  • Best-buy comparisons work because unit rates convert different packages into a fair comparison.
  • Scale drawings work because every length is enlarged or reduced by the same factor.

Common mistakes

  • Reversing the order of the ratio.
  • Dividing by the number of ratio parts instead of the total parts.
  • Comparing prices without converting to a unit rate.
  • Mixing units before simplifying.

Multiple methods

  • Ratio problems can be solved by bar models, tables, equivalent ratios or equations.
  • Best-buy problems can be solved by unit price or by scaling both options to a common amount.
  • Recipe problems can be solved by scaling the ingredient that is given.

Worked examples

Sharing in a ratio

Share $84 in the ratio 3 : 4.

Method: Find the value of one part.

  1. 1.Total parts = 3 + 4 = 7.
  2. 2.One part = 84 divided by 7 = 12.
  3. 3.3 parts = 36 and 4 parts = 48.

Answer: $36 and $48

Best buy

Which is cheaper: 3 kg for $12 or 5 kg for $18?

Method: Compare unit rates.

  1. 1.$12 divided by 3 = $4 per kg.
  2. 2.$18 divided by 5 = $3.60 per kg.
  3. 3.The lower unit rate is better value.

Answer: 5 kg for $18

Interactive practice

Try before you look

0/3 correct, 0 answered

Question 1

Simplify 18 : 24.

Question 2

Share 60 in the ratio 2 : 3.

Question 3

A car travels 180 km in 3 hours. What is its average speed?

Review prompt

Explain why unit rates make best-buy comparisons fair.

Write a two-sentence answer in your notebook before marking the workbook section complete.

Challenge question

Paint A mixes red and blue in the ratio 2 : 5. Paint B mixes red and blue in the ratio 3 : 8. Which paint has the greater fraction of red?

Hint: Compare red/total for each paint.