Chapter 16
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Chapter 16: Ratio and Proportion
16.1 Understanding Ratios
A ratio is a comparison of two numbers or quantities that shows their relative sizes. Ratios can be written in three different forms:
Using a colon ( a:b )
As a fraction ( a/b )
In words ( "a to b" )
Example 1:
If a class has 10 boys and 15 girls, the ratio of boys to girls is 10:15 or 10/15. This can be simplified to 2:3, meaning for every 2 boys, there are 3 girls.
Real-World Application:
Ratios are everywhere! Recipes use ratios (2 cups of flour for 1 cup of sugar), maps use ratios (1 cm represents 10 km), and sports statistics compare player performance.
16.2 Understanding Proportions
A proportion is an equation stating that two ratios are equal. If a/b = c/d, then the two fractions form a proportion.
Example 2:
A recipe needs 2 cups of sugar for 3 cups of flour. If you want to use 6 cups of flour, how much sugar should you use?
Set up a proportion:
23=x6frac{2}{3} = frac{x}{6}32=6x
Solve by cross multiplying:
2×6=3×x2 times 6 = 3 times x2×6=3×x12=3x12 = 3x12=3xx=4x = 4x=4
So, you should use 4 cups of sugar.
Real-World Application:
Proportions help in scaling drawings, resizing images, and even calculating discounts while shopping!
Exercises
A school has 300 students, and 120 are girls. Find the ratio of girls to boys.
A map scale is 1 cm = 5 km. What distance does 8 cm on the map represent in real life?
If 5 apples cost $2.50, how much would 8 apples cost?
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