Connect ratios with fractions of a whole

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Connect ratios with fractions of a whole

A ratio compares quantities in a stated order. If red:blue = 3:2, there are five equal shares in the total. Red accounts for 3/5 of the total and blue for 2/5. The fraction 3/2 compares red with blue, so it answers a different question.

To divide a total in a ratio, add the ratio parts, find one equal share, then multiply by the parts. Quantities must use compatible units before forming a ratio. A ratio 3 m:50 cm becomes 300:50 = 6:1, not 3:50.

An increase to one group can change the ratio even if another group stays fixed. State whether a problem fixes the total, fixes one quantity or merely describes a comparison. These constraints determine which fraction is useful.

Worked example: Divide £40 in the ratio 3:2.

There are 3 + 2 = 5 shares.

One share is £40 ÷ 5 = £8.

Multiply £8 by 3 and by 2.

Answer: £24 and £16.

Check your understanding: If boys:girls = 2:3, what fraction of the group are girls?

Answer: 3/5.

Why: The whole group has five equal shares, not two.