Grade 5 ↓
Ratios and Proportions
In math, ratios and proportions help us compare quantities. A ratio is a way of showing the relationship between two numbers, while a proportion tells us that two ratios are equal. In this guide, we'll explore these concepts using simple language and lots of examples.
Understanding ratios
A ratio compares two quantities. It tells us how much of one thing is compared to another. We usually write ratios as A:B or the fraction A/B. For example, if you have 2 apples and 3 oranges, the ratio of apples to oranges can be written as 2:3 or 2/3.
Example: If there are 4 cats and 6 dogs in a park, what is the ratio of cats and dogs?
Ratio of cats and dogs = 4:6 or 4/6.
Ratios can also be simplified the same way we simplify fractions. In the example of cats and dogs, 4:6 can be simplified to 2:3 by dividing both numbers by 2.
Example: Simplify the ratio 8:12.
Both numbers can be divided by 4: 8/4 and 12/4 we get 2:3.
Visual example: proportions
This image shows 2 blue squares and 3 green rectangles, indicating a 2:3 ratio.
Understanding ratios
A ratio is an equation that shows that two ratios are equal. For example, if 4 eggs are needed for two cakes and you want to make 4 cakes, you need 8 eggs. Therefore, the ratio can be written as 2:4 = 4:8 or 2/4 = 4/8.
Example: Are the ratios 6:9 and 2:3 proportional?
To check, simplify 6:9 to 2:3 (both can be divided by 3). Since both ratios are the same after simplifying, they are proportional!
How to solve proportion problems
When solving problems involving ratios, we often use cross-multiplication. If a/b = c/d, then a * d = b * c.
Example: Solve the ratio 3/4 = x/8.
3 * 8 = 4 * x
24 = 4x
X = 24/4
x = 6
So, x = 6 The ratios are equal when the value of x is 6.
Visual example: proportions
The first image shows a 1:2 ratio, and the second image maintains this ratio by doubling each side.
Uses of ratio and proportion in real life
Ratio and proportion are very useful tools in everyday life. You can use them for cooking, creating art, planning a trip, or creating an efficient budget.
Example: A recipe calls for 2 cups of flour for 3 cups of sugar. If you were to make double the amount, how much flour and sugar would you use?
Original ratio = 2:3
Double recipe = (2x2):(3x2)
= 4:6
You will need 4 cups of flour and 6 cups of sugar.
Practicing ratio and proportion
Practice is key to mastering ratios and proportions. Try making up your own examples or solving problems from worksheets and textbooks.
Practice problem: The ratio of boys and girls in a class is 5:6. If there are 20 boys, how many girls are there?
5/6 = 20/x
5 * x = 6 * 20
5x = 120
X = 120/5
x = 24
There are 24 girls in the class.
By understanding and practicing ratios and proportions, you will develop a stronger grasp on math, which will help you make comparisons and calculations in practical, everyday situations.
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