Ratio: Sharing Into Parts

What you will learn

• How to add ratio parts to find the total number of equal parts.
• How to find the value of one part.
• How to share a total into two parts.
• How to share a total into three parts.
• How to interpret which unequal share belongs to which person or category.
• How to check that your shares add back to the total.

Key facts before you start

Ratio sharing into parts infographic

Why this matters

Sharing into a ratio is useful when prize money is split, ingredients are mixed, groups are divided or distances are compared.

In exams, the method is often worth marks even when the numbers are simple. Clear working helps you avoid mixing up the bigger and smaller shares.

Prior knowledge

You should already be comfortable with:

• reading ratio notation such as 3 : 5,
• knowing that the order of a ratio matters,
• multiplying and dividing whole numbers,
• adding several parts accurately,
• checking whether an answer is sensible in context.

Clear explanation

The parts method

A ratio tells you how many equal parts belong to each share. To share a total in a ratio:

Sharing into two parts

Share £40 in the ratio 3 : 5. The total number of parts is:

Each part is worth:

Now multiply by each ratio part:

Sharing into three parts

The same method works for three-part ratios. Share 60 sweets in the ratio 2 : 3 : 5.

Interpreting unequal shares

If the question says Ali : Bea = 2 : 7, Bea gets the larger share because 7 parts is more than 2 parts.

Keep the names in the same order as the ratio. Do not swap the answers at the end.

A simple visual check

This bar shows £40 shared in the ratio 3 : 5. There are 8 equal boxes, so each box is £5.

Worked examples

Quick checks

Choose an answer, then check your thinking.

Practice questions

Answers and marking guidance

The exact practice answers are hidden under each question so you can try first. For sharing into a ratio, marks usually come from adding the total parts, finding the value of one part, multiplying each share correctly, and checking that the shares add back to the original total with the right units. When the question gives a difference between two shares, link that difference to the matching difference in ratio parts before finding one part.

Common mistakes

• Dividing by one ratio number: for 2 : 3, divide the total by 5 parts, not by 2 or 3.
• Forgetting a part in a three-part ratio: for 2 : 3 : 5, the total is 10 parts.
• Swapping the shares: keep names or categories in the same order as the ratio.
• Stopping before the check: the final shares should add back to the original total.
• Losing units: use £, g, kg, minutes or counters when the question gives units.

Extension challenge

A charity event raises £210. The money is shared between three causes in the ratio 4 : 5 : 6. The largest cause then donates £8 to the smallest cause. What is the new ratio of the three amounts?

Exam-board guidance

Sharing a quantity in a given ratio is common across GCSE Maths specifications. It may be tested directly or inside worded problems involving money, measurements, recipes, groups and proportional reasoning.

Next lesson

Next, connect ratio parts to fractions of a whole.