Introduction to Ratios
A ratio compares quantities to show their relative sizes, written as a : b. For example, 2 apples to 3 bananas is 2 : 3. To simplify, divide both parts by the same number, so 24 : 40 becomes 3 : 5.
Video Lesson
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What Is a Ratio?
- A ratio compares quantities and is written as a : b.
- The order matters (apples : bananas = 2 : 3, but bananas : apples = 3 : 2).
Working with Ratio 5:2
- A ratio of 5 : 2 means for every 5 parts of flour, there are 2 parts of sugar.
- To find one part, divide by 5 to get per part.
- Multiply by 2 to get of sugar needed.
Sharing a Whole in a Ratio
- Add the numbers in the ratio to find the total parts. For example, 7:3 means parts.
- Each part = total amount ÷ total parts. For example, £200 total divided by 10 parts = £20 per part.
- One person gets 7 parts, so £ £140. The other person gets 3 parts, so £ £60.
Simplifying and Expanding Ratios
- To simplify, divide every part by the same number. For example, 24:40 can be simplified by dividing both by 8 to get 3:5.
- To expand, multiply every part by the same number. For example, 3:7 can be expanded by multiplying both by 5 to get 15:35.
Practice Questions
Test your understanding
Simplify the ratio to its simplest form.
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The highest common factor of 18 and 24 is 6.
Divide both parts by 6: and .
So the ratio in its simplest form is .
If the ratio of apples to oranges is , how would you write the ratio of oranges to apples?
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The order of a ratio follows the order the quantities are named.
Apples to oranges is , so oranges to apples puts the oranges first: .
If £300 is split between two people in a ratio of , how much does the first person receive?
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The ratio has parts in total.
One part is £ £60.
The first person gets 3 parts: 3 × £ £180.
The ratio of pencils to pens in a box is . If there are 40 items in total, how many pencils are there?
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The ratio has parts in total.
One part is items.
Pencils take 5 parts: pencils (and pens take .
The ratio of red to blue marbles is . If there are 36 red marbles, how many blue marbles are there?
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The 4 red parts represent 36 marbles, so one part is marbles.
Blue takes 5 parts: blue marbles.
The ratio of adults to children at an event is . If there are 150 adults, how many people are there in total?
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The 5 adult parts represent 150 adults, so one part is people.
The total is parts: people.
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Interactive Activity
Simplifying and expanding ratios by finding equivalent forms
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Frequently asked questions
The questions students bump into most on this topic
A ratio compares two or more quantities and shows their relative sizes, written with a colon, a : b. With 2 apples and 3 bananas, the ratio of apples to bananas is 2 : 3. The order matters: bananas to apples is 3 : 2. Ratios can be simplified and expanded like fractions without changing what they mean.
Find the value of one part, then multiply. A cake needs flour and sugar in the ratio 5 : 2, so 5 parts of flour go with 2 parts of sugar. With 300 g of flour, the 5 parts are 300 g, so one part is 300 ÷ 5 = 60 g. The sugar is 2 parts: 2 × 60 = 120 g.
Add the parts, divide the amount by that total to find one part, then multiply by each person’s parts. To share £200 in the ratio 7 : 3: there are 10 parts, so one part is £200 ÷ 10 = £20; you get 7 × £20 = £140 and your friend 3 × £20 = £60. Check: £140 + £60 = £200.
Divide every part by the same number, and repeat until the parts share no factor but 1. For 24 : 40, divide by 4 to get 6 : 10, then by 2 to get 3 : 5. Expanding is the reverse: multiply every part by the same number, so 3 : 7 times 5 is 15 : 35. The numbers change but the ratio stays the same.
24 : 36 simplifies to 2 : 3, because both numbers divide by 12. The same method works for any pair: 8 : 12 is also 2 : 3, 6 : 8 is 3 : 4, and 18 : 20 is 9 : 10. Find the biggest number that divides into both parts and divide each part by it.
What's next?
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