JENECONKMaths Universe

Ratios

Ages 10–15

Difficulty adapts to you

Ratios

A ratio compares quantities in the same order. Equivalent ratios are made by multiplying or dividing every part by the same number.

Your goals

  • ✓You can describe and simplify relationships between quantities.
  • ✓You can use ratio, equivalent ratio correctly.
  • ✓You can keep the quantities in the stated order.

Words to know

ratio:
A comparison of quantities written in a fixed order.
equivalent ratio:
A ratio made by scaling every part by the same non-zero factor.

Examples

  • 18 red beads to 12 blue beads is 8:12 = 2:3.
  • 2If flour:sugar is 3:1, then 600 g of flour needs 200 g of sugar.

More than one way to solve it

Try each method, then choose the one you can explain and check most clearly.

Method 1

Unitary method

Best for: Scaling to any amount
  1. 1.Find the value of one part.
  2. 2.Multiply by the required number of parts.
  3. 3.Check the ratio remains equivalent.

Example: If 3 books cost ₦1,500, one costs ₦500 and 7 cost ₦3,500.

Method 2

Ratio table

Best for: Seeing equivalent ratios
  1. 1.Write matching quantities in two rows.
  2. 2.Scale both rows by the same factor.
  3. 3.Read the required value.

Example: 2:5 becomes 4:10, 6:15, and 8:20.

Check these

  • • Do not scale only one part of the ratio.
  • • Keep every number, symbol, label, and unit in its correct place.
  • • Choose the method that makes each step easiest to explain and check.

Helpful habits

  • • Read the whole question before choosing what to do.
  • • Show one clear step at a time and check each step.
  • • If you are stuck, draw a model, try smaller numbers, or revisit the example.

Now try your own

Create your own ratios example, solve it, and explain how you checked it.

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Helpful Hints

“If you are stuck, skip and come back later.”