L1 · Ratios: comparing two quantities

Learning goal

“I can write a ratio to compare two quantities - part to part and part to whole - and I know the order of the numbers matters, because each number stands for a named quantity.”

Ratio — a comparison of two quantities, written with a colon, like 3 : 5, read '3 to 5.'

Term — each number in a ratio. In 3 : 5, the terms are 3 and 5.

Part-to-part ratio — compares one part of a group with another part (red marbles to blue marbles).

Part-to-whole ratio — compares one part with the whole group (red marbles to all marbles).

Worked example

A fruit bowl holds 4 apples and 6 oranges. Step 1: Name what is being compared, in order: apples first, oranges second. Step 2: The ratio of apples to oranges is 4 : 6. Step 3: Swap the order and the meaning changes: oranges to apples is 6 : 4 - a different ratio. On the double number line, one line is marked 0, 4 (apples) and the other 0, 6 (oranges) - same starting point, different counts, so the comparison is visible. A ratio is not two loose numbers: each term stands for a named quantity, in a named order.

Check yourself — explain it

In the ratio 4 : 6 for this fruit bowl, what does the 4 stand for?

Paired problem — example still visible

A class has 5 boys and 7 girls. Write the ratio of boys to girls -> 5 : 7

Faded completion — last step is yours

"There are 2 cats and 9 dogs. The ratio of cats to dogs is ___ : ___" -> 2 : 9

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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