1. Ratios, Proportions, and Percents

2. Ratios A ratio compares two quantities.
A ratio can be written in three ways.
Write ratios in their simplest form.
The number of hearts (5) to lightning bolts (4) can be written 5:4, 5 to 4, or 5/4.
The ratio of stars (6) to lightning bolts (4) needs to be simplified. It can be written 3:2, 3 to 2, or 3/2.
Write the ratio of hearts to total objects in three ways.

3. Ratios A ratio compares two quantities.
A ratio can be written in three ways.
Write ratios in their simplest form.
The number of hearts (5) to lightning bolts (4) can be written 5:4, 5 to 4, or 5/4.
The ratio of stars (6) to lightning bolts (4) needs to be simplified. It can be written 3:2, 3 to 2, or 3/2.
Write the ratio of hearts to total objects in three ways.
1:3, 1 to 3, 1/3

4. the cross products are equal
Proportions
A proportion is a statement that two ratios are equivalent.
Two ratios form a proportion if:
the cross products are equal
the units are the same
5×16 and 4×20 are cross products.
Each ratio compares hearts to lightning bolts.
The cross products are equal.

5. Use Proportions to Solve Problems
Step 1: Let n equal the unknown quantity.
Step 2: Set up a proportion.
Step 3: Use cross products to solve.
Problem: Jenna can buy 150 cell phone minutes for $12.
What will she pay for 225 cell phone minutes?
Step 1: Let n equal the cost for 225 minutes.
Step 3: × n = 12 × 225
150n = 2700 =
Step 2:
n = 18
Jenna will pay $18 for 225 minutes.

6. Use Proportions to Solve Problems
Step 1: Let n equal the unknown quantity.
Step 2: Set up a proportion.
Step 3: Use cross products to solve.
Use a proportion to solve. Show your work.
Adam rode his bicycle 105 miles in 3 hours.
How many miles did he ride in 2 hours?

7. Use Proportions to Solve Problems
Step 1: Let n equal the unknown quantity.
Step 2: Set up a proportion.
Step 3: Use cross products to solve.
Use a proportion to solve. Show your work.
Adam rode his bicycle 105 miles in 3 hours.
How many miles did he ride in 2 hours?
105 miles
2 hours
n miles
3 hours =
3 × n = 105 × 2
3n = 210 3n 3
210
n = 70

8. You can use a proportion to solve percent problems.
Percents
A percent is a ratio in which the first term of the ratio is compared to 100.
You can use a proportion to solve percent problems.
Example: 7% = 7 to 100, 7:100, or 7/100
What is 35% of 80?
35% of 80 is 28.
What is 12% of 125?
36 is 45%
of what number?
15 is what percent of 75?

9. You can use a proportion to solve percent problems.
Percents
A percent is a ratio in which the first term of the ratio is compared to 100.
You can use a proportion to solve percent problems.
Example: 7% = 7 to 100, 7:100, or 7/100
What is 35% of 80?
35% of 80 is 28.
What is 12% of 125?
36 is 45%
of what number?
15 is what percent of 75? 15 80
20%

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