Ratio notation and part-to-part/whole meaning | Year 7

01 / LEARN

The idea, step by step

A ratio compares amounts

The ratio $3 : 2$ is read “3 to 2”. In the picture, blue:yellow is $3 : 2$ . The order of the labels determines the order of the numbers. Yellow:blue is $2 : 3$ . A ratio can compare counts, masses, lengths or other quantities.

The whole includes every part

There are $3 + 2 = 5$ counters altogether. Blue:all is therefore $3 : 5$ , and the fraction that is blue is $3 / 5$ . Part-to-part and part-to-whole comparisons answer different questions. Name both quantities before writing a ratio. For two measurements of the same kind, first use a common unit.

A common trap

For 4 green and 7 white marbles, writing the green fraction as $4 / 7$ .

Instead: The whole has 11 marbles. $4 : 7$ compares green with white; $4 / 11$ is the fraction of all marbles that are green.

02 / WORKED EXAMPLES

See the thinking

Example 1

Read the requested order

A bag has 4 green marbles and 7 white marbles. Write green:white, white:green and green:all.

Green:white keeps green first, giving $4 : 7$ .
Reverse the entries for white:green: $7 : 4$ .
There are $4 + 7 = 11$ altogether, so green:all is $4 : 11$ .

4 : 7

7 : 4

4 : 11

Example 2

Convert a measurement first

Two ribbons are 80 cm and 1 m long. Write the first ribbon:second ribbon ratio.

Convert 1 m to 100 cm.
Write $80 : 100$ in the requested order.
Divide both entries by 20 to obtain $4 : 5$ .

4 : 5

Check your understanding

There are 6 cats and 4 dogs. What is cats:all animals?

Show answer

$6 : 10$ , or $3 : 5$ .

All animals means $6 + 4 = 10$ , not just the four dogs.

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

There are 5 red counters and 3 blue counters. Write red:blue.
2 marks
There are 8 apples and 2 pears. Write pears:apples.
2 marks
A class has 12 students who walk and 8 who cycle. Write walkers:all students.
2 marks
In the counter picture, what fraction of the counters is yellow?
2 marks
A short string is 30 cm and a long string is 1.2 m. Write short:long in simplest form.
3 marks
Flour:sugar is $4 : 1$ . Is sugar one-quarter or one-fifth of the combined flour and sugar? Explain.
3 marks

Read the worked solutions

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

There are 5 red counters and 3 blue counters. Write red:blue.
2 marks
Put red first and blue second.
$5 : 3$ .
There are 8 apples and 2 pears. Write pears:apples.
2 marks
Pears comes first: $2 : 8$ .
Divide both entries by 2 for simplest form.
$2 : 8$ , or $1 : 4$ .
A class has 12 students who walk and 8 who cycle. Write walkers:all students.
2 marks
There are $12 + 8 = 20$ students.
Write $12 : 20$ and divide both entries by 4.
$12 : 20$ , or $3 : 5$ .
In the counter picture, what fraction of the counters is yellow?
2 marks
There are 2 yellow counters out of 5 altogether.
$2 / 5$ .
A short string is 30 cm and a long string is 1.2 m. Write short:long in simplest form.
3 marks
Convert 1.2 m to 120 cm.
Simplify $30 : 120$ by dividing both entries by 30.
$1 : 4$ .
Flour:sugar is $4 : 1$ . Is sugar one-quarter or one-fifth of the combined flour and sugar? Explain.
3 marks
There are $4 + 1 = 5$ parts altogether.
Sugar is one of those five parts.
One-fifth.

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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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