Ratio, proportion & algebra
Ratio and Proportion: Scaling, Sharing, and Recipes
Year 3 · Year 4 · Year 5 · Year 6
- ✓Understand what a ratio is and how to write it using correct notation.
- ✓Use scale factors to enlarge or reduce quantities in practical problems.
- ✓Solve problems involving sharing a total amount into unequal parts based on a given ratio.
- ✓Adapt ingredient quantities in recipes to serve different numbers of people.
Key concepts
A ratio compares quantities of two or more things. It shows how much of one thing there is compared to another. We write ratios using a colon, for example, 1:2. The order of the numbers in a ratio is very important!
When two ratios are equivalent, they are in proportion. This means that if you multiply or divide one side of a ratio by a number, you must do the same to the other side(s) to keep the relationship the same.
A scale factor is a number used to multiply all quantities in a ratio to make them larger (enlarge) or smaller (reduce) while keeping the proportion the same. For example, if a scale factor is 2, you multiply everything by 2. If it's 0.5 (or 1/2), you halve everything.
Sometimes we need to share a total amount into parts that are not equal, but follow a specific ratio. For example, sharing 10 sweets in the ratio 3:2 means one person gets 3 parts and the other gets 2 parts out of the total.
Recipes often tell you the ingredients needed for a certain number of servings. Using ratios and scale factors, you can change the amounts of all ingredients so the recipe makes more or less food, but still tastes the same.
Key facts to remember
- 1A ratio compares two or more quantities.
- 2The order of numbers in a ratio is important.
- 3Ratios can often be simplified by dividing all parts by a common factor.
- 4A scale factor multiplies all parts of a ratio to change its size (enlarge or reduce).
- 5When sharing unequally, first add the parts of the ratio to find the total number of shares.
- 6To keep things in proportion, if you change one part of a ratio, you must change all other parts by the same scale factor.
Worked examples
Example 1
A drawing of a flower has a stem that is 6 cm long. If you want to enlarge the drawing by a scale factor of 2, how long will the stem be in the new drawing?
Answer
The stem in the new drawing will be 12 cm long.
Remember to multiply ALL measurements by the scale factor if you were enlarging the whole drawing.
Example 2
Share 25 pencils between Sarah and Tom in the ratio 3:2. How many pencils does each child get?
Answer
Sarah gets 15 pencils and Tom gets 10 pencils.
You can check your answer by adding the individual amounts: 15 + 10 = 25, which is the total number of pencils.
Example 3
A recipe for 6 cupcakes needs 150g of flour. How much flour is needed if you want to make 18 cupcakes?
Answer
You will need 450g of flour to make 18 cupcakes.
You would need to multiply all other ingredients by the same scale factor (3) to keep the recipe in proportion.
Common mistakes
- ✗Mixing up the order of the quantities in a ratio (e.g., writing 2:3 instead of 3:2).
- ✗Only changing one part of a ratio when using a scale factor, instead of all parts.
- ✗For unequal sharing, forgetting to add the ratio parts first to find the total number of shares before dividing.
- ✗Not simplifying ratios to their simplest form when asked to do so.
Exam tips
- ★Always read the question carefully to understand exactly what is being asked.
- ★Show all your working steps clearly so the examiner can follow your maths.
- ★Check your answer to make sure it makes sense in the context of the problem.
- ★Draw pictures or diagrams to help you understand and solve ratio problems, especially for sharing.
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