RatiosProportionsPercents.ppt
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Ratios, Proportions,
and Percents
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.
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
Proportions
A proportion is a statement that two ratios are equivalent.
Two ratios form a proportion if:
the units are the same
the cross products are equal
5 hearts
20 hearts
4 lightning bolts 16 lightning bolts
5 20
4 16
Each ratio compares
hearts to lightning bolts.
5×16 and 4×20 are cross products.
5 16 ? 4 20
80 80
The cross products are equal.
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 2:
150 minutes
225 minutes
=
$12
n
Step 3: 150 × n = 12 × 225
150n = 2700
150n 2700
=
150
150
n = 18
Jenna will pay $18
for 225 minutes.
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?
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
3 hours
n miles
=
2 hours
3 × n = 105 × 2
3n = 210
3n
3
=
210
n = 70
3
Percents
A percent is a ratio in which the first term of the ratio is compared to 100.
Example: 7% = 7 to 100, 7:100, or 7/100
You can use a proportion to solve percent problems.
What is 35% of 80?
n
35
80 100
100 n 35 80
100n 2800
35% of 80 is 28.
100n 2800
100
100
n 28
What is 12% of 125?
36 is 45%
of what number?
15 is what percent
of 75?
Percents
A percent is a ratio in which the first term of the ratio is compared to 100.
Example: 7% = 7 to 100, 7:100, or 7/100
You can use a proportion to solve percent problems.
What is 35% of 80?
n
35
80 100
100 n 35 80
100n 2800
35% of 80 is 28.
100n 2800
100
100
n 28
What is 12% of 125?
15
36 is 45%
of what number?
80
15 is what percent
of 75?
20%
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