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.
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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
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Simplify the ratio to its simplest form.
Correct! 🎉 +10 pointsNot quite right
Dividing both numbers by their highest common factor 6. Then and , resulting in .
If the ratio of apples to oranges is , how would you write the ratio of oranges to apples?
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The ratio of oranges to apples is simply the reverse of the ratio of apples to oranges, which is .
If £300 is split between two people in a ratio of , how much does the first person receive?
Correct! 🎉 +20 pointsNot quite right
Dividing £300 by 5 gives £60 per part, and then multiply by 3: .
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 of pencils to pens is , so the total ratio of parts is . To find the number of pencils, calculate .
The ratio of red to blue marbles is . If there are 36 red marbles, how many blue marbles are there?
Correct! 🎉 +20 pointsNot quite right
The ratio of red to blue marbles is . If 4 parts equal 36, each part is . So the blue marbles are .
The ratio of adults to children at an event is . If there are 150 adults, how many people are there in total?
Correct! 🎉 +30 pointsNot quite right
If 5 parts equal 150 adults, each part is . The total is 8 parts, so .
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Interactive Activity
Simplifying and expanding ratios by finding equivalent forms
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Yes, the order matters. The first number always refers to the first quantity you name. With 2 apples and 3 bananas, the ratio of apples to bananas is 2:3, but the ratio of bananas to apples is 3:2. Swapping the numbers changes what the ratio describes.
A ratio like 5:2 tells you how many parts of each quantity you have. In a 5:2 flour to sugar recipe, every 5 parts of flour go with 2 parts of sugar. The parts can be any equal size, as long as you keep that pairing.
Add the parts to find the total number of parts, then divide the amount by that total to find the value of one part. Multiply by each share's parts. Sharing £200 in the ratio 7:3 gives £20 a part, so £140 and £60.
To simplify a ratio, find a common factor of all the parts and divide each part by it. Repeat until the parts share no factor other than 1. For example, 24 to 40 divides by 4 to give 6 to 10, then by 2 to reach 3:5.
Multiply every part of the ratio by the same number. This expands the ratio while keeping the same proportion, so the new ratio is equivalent. For example, multiplying 3 to 7 by 5 gives 15 to 35, which is an equivalent ratio.
Simplifying or expanding changes only the size of the numbers, not the proportion between the parts. You divide or multiply every part by the same number, so each quantity keeps the same share. That is why 24:40, 6:10 and 3:5 all describe one ratio.