NAME _____________________________________________ DATE ____________________________ PERIOD _____________
7-1 Study Guide and Intervention
Ratios and Proportions
Write and Use Ratios A ratio is a comparison of two quantities by divisions. The ratio a to b, where b is not zero, can
𝑎
be written as 𝑏 or a:b.
Example 1: In 2007 the Boston RedSox baseball team won 96 games out of 162 games played. Write a ratio for the
number of games won to the total number of games played.
Example 2: The ratio of the measures of the angles in △JHK is 2:3:4. Find the measures of the angles.
Exercises
1. In the 2007 Major League Baseball season, Alex Rodriguez hit 54 home runs and was at bat 583 times.
What is the ratio of home runs to the number of times he was at bat?
2. There are 182 girls in the sophomore class of 305 students. What is the ratio of girls to total students?
3. The length of a rectangle is 8 inches and its width is 5 inches. What is the ratio of length to width?
4. The ratio of the sides of a triangle is 8:15:17. Its perimeter is 480 inches. Find the length of each side of the triangle.
5. The ratio of the measures of the three angles of a triangle is 7:9:20. Find the measure of each angle of the triangle.
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
7-1 Study Guide and Intervention (continued)
Ratios and Proportions
Use Properties of Proportions A statement that two ratios are equal is called a proportion.
𝑎
𝑐
In the proportion 𝑏 = 𝑑, where b and d are not zero, the values a and d are the extremes and the
values b and c are the means. In a proportion, the product of the means is equal to the product
of the extremes, so ad = bc. This is the Cross Product Property.
𝑎
𝑏
𝑐
=𝑑
a⋅d=b⋅ c
extremes means
Example 1: Solve
𝟗
𝟏𝟔
=
𝟐𝟕
.
𝒙
Example 2: POLITICS Mayor Hernandez conducted a random survey of 200 voters and found that 135 approve
of the job she is doing. If there are 48,000 voters in Mayor Hernandez’s town, predict the total number of voters
who approve of the job she is doing.
Exercises
Solve each proportion.
1
1. 2 =
3
28
𝑥
3
𝑦
2. 8 = 24
9
4. 18.2 = 𝑦
5.
2𝑥 + 3
8
5
=4
3.
𝑥 + 22
𝑥+2
6.
𝑥+1
𝑥–1
30
= 10
3
=4
7. If 3 DVDs cost $44.85, find the cost of one DVD.
8. BOTANY Bryon is measuring plants in a field for a science project. Of the first 25 plants he measures, 15 of them are
smaller than a foot in height. If there are 4000 plants in the field, predict the total number of plants smaller than a foot
in height.