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Year 7 Maths | Understand, justify, check

Scale a ratio without changing the relationship

Ratios compare quantities while rates connect quantities with different units. A recipe can keep its flavour as it grows, and a price can be compared per kilogram. In both cases, identify what must stay in proportion.

What to notice

A ratio of 2:3 contains five parts altogether. A rate of dollars per kilogram describes the cost of one kilogram, not the cost of the entire purchase.

What to do

Find the size of one ratio part or one unit of the rate. Scale from that unit to the requested amount. Keep labels attached to both sides of the comparison.

Why it works

A common scale factor preserves a ratio. Adding the same number to both terms usually does not. Unit rates make different-sized purchases comparable because their reference quantity is the same.

Work through an example

Red and blue tiles are in the ratio 2:3. There are 20 tiles. How many are red?

0Red8Blue12
Twenty tiles in a 2:3 ratio: 8 red and 12 blue. Bars start at zero.
  1. There are 2 + 3 = 5 equal ratio parts.
  2. Each part contains 20 ÷ 5 = 4 tiles.
  3. Red occupies two parts: 2 × 4 = 8 red tiles.

A common mistake

Dividing the total by only one ratio term overlooks the other group. Count every part before sharing the total.

A strategy to try

Check the result by rebuilding the whole. Eight red and twelve blue tiles total twenty, and both original ratio terms were multiplied by four.

Try it now

Try three questions

No account is needed. These examples do not change saved learning progress. Choose an answer and check it for an explanation; you can try again.

1. Cord A and cord B have lengths in the ratio 2:5. Cord A is 6 m. How long is cord B?
Help: a starting point

Compare the known length of cord A with its ratio term.

Help: the next step

Apply that same scale factor to the term for cord B.

2. Three kilograms of rice cost $7.50. What is the price per kilogram?
Help: a starting point

Per kilogram means the price of one kilogram.

Help: the next step

Share the total cost equally across the three kilograms.

3. A 28-person group has adults and students in the ratio 1:3. How many students are there?
Help: a starting point

Count the total ratio parts represented by adults and students.

Help: the next step

Find one part, then take the three student parts.

For parents and carers

Ask which quantity is fixed: the total, a group size or a rate. Encourage a small table before calculating. The later linear-relationship lesson connects a constant rate with a graph and an equation.

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