Ratio with fractions & percentage

The hardest P6 ratio problems mix ratio with fractions or percentages. Don't rush — take it one step at a time. First use the ratio to find the amounts (find one unit, then scale), then apply the fraction or percentage to the amount you found. Writing down what each step gives you keeps the working clear and avoids slips.

Worked example

Problem Ann and Ben share $20 in the ratio 2 : 3. Ann spends 1/4 of her share. How much has she left?

Share first: 2 + 3 = 5 units, so 1 unit = $20 ÷ 5 = $4. Ann's share = 2 × $4 = $8.
Apply the fraction: Ann spends 1/4 of $8 = $8 ÷ 4 = $2.
Ann has $8 − $2 = $6 left.
Watch out Take the fraction of the share, not of the total amount shared.
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