How it works
A ratio tells us how much of one thing there is compared to another. For example, if the ratio of red to blue flowers is 7:20, this means for every 7 red flowers, there are 20 blue flowers.
When you know how many of one color there actually are, you can use the ratio to find out how many of the other color there should be.
How to solve:
-
Write the ratio as a fraction. For red to blue, it's 7:20, or 7/20.
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Set up the proportion. If you know there are 84 red flowers, set up the equation: 7 red / 20 blue = 84 red / x blue
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Find the multiplier. Figure out how many times the given number (84) is bigger than the original ratio number (7): 84 divided by 7 = 12
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Multiply the blue side by the same number. 20 blue x 12 = 240 blue
So, if there are 84 red flowers, there are 240 blue flowers.
This method works for any ratio problem where you know one part and need to find the other!
Worked example
If the ratio of apples to oranges is 3:5, and there are 21 apples, how many oranges are there?
- 1
Write the ratio as a fraction.
The ratio is 3 apples to 5 oranges, so 3/5.
- 2
Set up the proportion.
We know 3 apples / 5 oranges = 21 apples / x oranges.
- 3
Find the multiplier.
21 divided by 3 = 7, so the ratio is multiplied by 7.
- 4
Multiply the oranges by the same number.
5 oranges x 7 = 35 oranges.
Answer
There are 35 oranges.
Common mistakes
- 01
Adding the numbers in the ratio instead of multiplying.
Why: Students might think they should just add the numbers together.
Avoid it: Remember, ratios are about comparing parts, not adding them together.
- 02
Dividing when they should multiply (or vice versa).
Why: Students mix up the order of operations.
Avoid it: Always divide first to find the multiplier, then multiply the other side of the ratio.
- 03
Mixing up which number goes with which object.
Why: Students forget which part of the ratio is which.
Avoid it: Label each part of the ratio carefully (e.g., apples, oranges).
Practice
Answers stay hidden
1.The ratio of dogs to cats is 4:9. If there are 36 dogs, how many cats are there?
Show hint
First, find how many times 4 goes into 36.
Reveal answer
81 cats
2.In a bag, the ratio of green marbles to yellow marbles is 2:7. If there are 18 green marbles, how many yellow marbles are there?
Show hint
Divide 18 by 2 to find the multiplier.
Reveal answer
63 yellow marbles
3.A class has a ratio of boys to girls as 5:8. If there are 40 boys, how many girls are there?
Show hint
How many times does 5 go into 40? Use that number to multiply the girls' ratio part.
Reveal answer
64 girls