Rukasha Maths

GCSE maths Beta

Ratio, sharing and recipes · Revision guide

Foundation · Ratio · 1 page in the PDF

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Learning objectives

  • Simplify ratios and divide an amount in a ratio.
  • Scale every ingredient in a recipe consistently.

Key ideas

Convert quantities to matching units before simplifying a ratio.

Divide every ratio part by the same common factor.

The first share is this fraction of the total.

a:b⟹aa+ba:b\quad\Longrightarrow\quad\frac{a}{a+b}

Find one part by dividing the total by the sum of all ratio parts.

Multiply every recipe ingredient by the same scale factor.

k=new portionsoriginal portionsk=\frac{\text{new portions}}{\text{original portions}}

Worked examples

Example 1

Share the money in the given ratio.

£84 in ratio 2:5:2+5=7 parts\text{£84 in ratio }2:5:\qquad2+5=7\ \text{parts}
one part=£847=£12\text{one part}=\frac{\text{£84}}7=\text{£12}
2(£12)=£24,5(£12)=£602(\text{£12})=\text{£24},\qquad5(\text{£12})=\text{£60}
£24 and £60\text{£24 and £60}

Example 2

Scale flour from four portions to ten portions.

k=104=2.5,300 g×2.5=750 gk=\frac{10}{4}=2.5,\qquad300\text{ g}\times2.5=750\text{ g}
750 g750\text{ g}

Watch out

When sharing a total, divide by the sum of all ratio parts. The individual parts are not separate denominators.