5.1 Ratio notation, simplifying and sharing — Learn

Prerequisites

You should be able to multiply and divide whole numbers and fractions. Check units before comparing quantities.

Key terms

A ratio compares quantities by division. The unitary method finds the value of one equal part.

Objectives

• Write equivalent ratios, simplify them and share a total in a given ratio.
• Check that the result matches the units and direction of change.

Learn the method

A ratio compares amounts by division. In $3:5$, there are 3 parts of the first amount for every 5 parts of the second. Multiply or divide every part by the same non-zero number to make an equivalent ratio. To share a total, add the parts, divide the total by their sum, then multiply by each part count.

Worked example. The ratio of red counters to blue counters is $3:5$. What fraction of the blue count is the red count?

• Compare red with blue: $\frac{3}{5}$.
• The red count is $\frac{3}{5}$ of the blue count.

Worked example. A class has 8 pupils who walk and 12 who travel by bus. Express the number who travel by bus as a fraction of the number who walk.

• Write bus:walk as a fraction: $\frac{12}{8}$.
• Simplify: $\frac{12}{8}=\frac{3}{2}$.
• The fraction is greater than 1 because more pupils travel by bus than walk.

Worked example. Share £64 in the ratio $3:5$.

• Add the parts: $3+5=8$.
• Find one part: $64\div8=8$.
• First share: $3\times8=24$.
• Second share: $5\times8=40$.
• Check: $24+40=64$.

Worked example. Share 40 counters in the ratio 3:5, where 3 parts are red and 5 parts are the total.

• The ratio is part:whole, so red is $\frac{3}{5}$ of the total.
• Red counters: $40\times\frac{3}{5}=24$.
• Blue counters: $40-24=16$.
• Check: $24:40=3:5$.

A unitary method finds the value of one part first. For example, 24 counters in ratio $3:5$ have 8 total parts. One part is $24\div8=3$, so the second amount is $5\times3=15$.

Watch out. Do not add the same number to both ratio parts. That changes the quotient. Divide each part by the same factor, then check that the simplified ratio has the same quotient.

You should now be able to

• I can simplify ratios by multiplying or dividing each part by the same factor.
• I can find one part and share a total in a given ratio.
• I can check that my shares add to the original total.