Ratio tables | Year 7 | Ascent Library

01 / LEARN

The idea, step by step

Each pair has meaning

A ratio table records quantities linked in a fixed proportion. If three tickets cost 12 dollars, six cost 24 dollars and nine cost 36 dollars. The unit cost is 4 dollars per ticket. Keep quantities and units in labelled rows or columns. A pair taken from different columns would not represent a linked purchase.

Choose a useful calculation

Multiply a known pair, divide to find one unit, or combine compatible pairs. Choose a route with simple arithmetic and check the resulting unit value. Numbers that increase regularly are not automatically proportional: a fixed entry fee can make a cost table rise by equal amounts while the total cost is not a fixed multiple of quantity.

A common trap

Adding 2 dollars when increasing from 3 notebooks to 5 notebooks.

Instead: At 4 dollars each, two extra notebooks add 8 dollars, not 2 dollars. The new total is 20 dollars.

02 / WORKED EXAMPLES

See the thinking

Example 1

Scale and use a unit price

Three identical notebooks cost 12 dollars. Find the costs of 6 and 10 notebooks.

Identical notebooks
Notebooks	3	6	10
Cost (dollars)	12	?	?

Six is twice three, so its cost is 24 dollars.
One notebook costs $12 / 3 = 4$ dollars.
Ten notebooks cost $10 (4) = 40$ dollars.

6 cost 24 dollars; 10 cost 40 dollars.

Example 2

Find a row that does not fit

A table contains $(2, 8)$ , $(4, 16)$ and $(5, 22)$ . Does it keep one ratio?

The first two pairs have second entry four times the first.
For 5, the second entry should be $5 (4) = 20$ .
The listed 22 does not fit.

No. Replace

(5, 22)

with

(5, 20)

to keep the ratio.

Check your understanding

Four identical pens cost 10 dollars. Find the cost of 12 pens.

Show answer

30 dollars.

Twelve is three times four, so multiply the linked cost by three.

03 / WORKSHEET

Your turn

6 questions · 15 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Two identical bottles hold 3 L altogether. How much do 6 hold?
2 marks
Five identical rulers cost 15 dollars. Find the costs of 1 ruler and 8 rulers.
2 marks
For red:blue $3 : 4$ , complete $(3, 4)$ , $(6, □)$ , $(□, 20)$ .
2 marks
A map uses 1 cm for 5 km. Find the distances for 3 cm, 7 cm and 10 cm.
3 marks
Hours and pay are $(1, 18)$ , $(2, 36)$ , $(3, 54)$ and $(4, 70)$ . Which entry breaks a fixed hourly-rate model?
3 marks
Two equal rows have 8 seats. Find seats in 3, 5 and 7 such rows.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Two identical bottles hold 3 L altogether. How much do 6 hold?
2 marks
Multiply both bottle count and total volume by 3.
9 L.
Five identical rulers cost 15 dollars. Find the costs of 1 ruler and 8 rulers.
2 marks
One costs $15 / 5 = 3$ dollars.
Eight cost $8 (3) = 24$ dollars.
3 dollars and 24 dollars.
For red:blue $3 : 4$ , complete $(3, 4)$ , $(6, □)$ , $(□, 20)$ .
2 marks
Double the known pair for $(6, 8)$ .
Multiply by 5 for $(15, 20)$ .
8 and 15.
A map uses 1 cm for 5 km. Find the distances for 3 cm, 7 cm and 10 cm.
3 marks
Multiply each map length by 5 km per centimetre.
15 km, 35 km and 50 km.
Hours and pay are $(1, 18)$ , $(2, 36)$ , $(3, 54)$ and $(4, 70)$ . Which entry breaks a fixed hourly-rate model?
3 marks
The first three pairs give 18 dollars per hour.
Four hours should give $4 (18) = 72$ dollars.
70 dollars for 4 hours; the matching pay is 72 dollars.
Two equal rows have 8 seats. Find seats in 3, 5 and 7 such rows.
3 marks
One row has $8 / 2 = 4$ seats.
Multiply 4 by 3, 5 and 7.
12, 20 and 28 seats.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Year 7 ratio comparisons and practical proportional models, including units, part-to-whole meaning and assumptions.

Official curriculum source ↗

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