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• Ratio problems take different forms, which may include:

  • linking ratios and fractions

  • part-part problems - where the value of one part of the ratio is given and the value of another ratio part has to be found

  • part-whole problems - where the value of one part of the ratio is given and the value of the whole has to be found

  • comparison problems - where the ratio and the difference between the values is given

  • problems where values change, giving a new ratio

• In order to solve ratio problems, an understanding of the structure of the problem is needed. A bar model may help to clarify this.

• An understanding of equivalent ratios and simplifying ratios, as well as division in a given ratio is needed to solve ratio problems.

To solve a problem involving ratios and fractions, you may be given the ratio or the fraction.

When given the ratio:

• Add the ratio parts together to find the denominator of the fraction.

• The numerator of the fraction is the ratio part that is the focus of the question.

When given the fraction:

• The numerator of the fraction gives one of the ratio parts.
• Find the other ratio part by subtracting the numerator from the denominator.
• Write the ratio in the correct order.

A part-part ratio problem is where the value of one part of the ratio is given and the value of another ratio part has to be found. A part-whole problem is where the value of one part of the ratio is given and the value of the whole has to be found.

Given a ratio and the value of one part of the ratio, find the value of another ratio part or the value of the whole.

1. Draw a bar model split into the total number of parts. Label with the given information to represent the problem.

2. Find the value of one part by dividing the given value by the associated number of parts.

   • To find the value of another ratio part in a part-part problem, multiply the value of one part by the number of parts asked for.

   • To find the whole in a part-whole problem, multiply the value of one part by the total number of parts.

Some ratio problems involve a comparison between values. The comparison is the value difference between two parts of the ratio.

Given a ratio and a comparison between values:

1. Draw a bar model to illustrate the problem.

2. Label the given information.

3. Find the value of one part by dividing the comparison value by the number of parts given.

4. Multiply the value of one part by the number of parts of the object of the question.

Given a ratio and total amount, find the new changing amounts and find the new ratio:

1. A total amount and ratio is given. Draw a bar model to illustrate this starting information.

2. Divide the total amount in the initial ratio.

   • Find the value of one part by dividing the total amount by the sum of the parts.
   • Multiply the value of one part by the number of parts for each share of the ratio.

3. Adjust the shared amounts according to the given information in the question.

4. Write the new amounts as a ratio and simplify, if necessary, by dividing the parts by their highest common factor (HCF).

In this example, you need to be able to divide in a given ratio and simplify ratios.

Practise solving ratio problems in this quiz. You may need a pen and paper to complete these questions.

Ratio problems occur in many different contexts.

• Successful cookery relies on the ratio of the ingredients used. For example:

  • To make meringues, you need a ratio of 2 parts sugar to 1 part egg white.

  • To make Yorkshire puddings, you need equal amounts of egg, flour and milk (and a pinch of salt). The ratio of egg, flour and milk is 1 : 1 : 1

• In construction, fencing companies use a fixed ratio of concrete mix to water to secure fence posts. For a given amount of concrete mix, the amount of water needed is worked out. This is a part-to-part ratio problem.