Study Guide:
Ratios and Proportions
In mathematics, a ratio compares two numbers by division. A ratio that compares a number a to a number b can be written in the following ways.
When a ratio compares two quatitites with different unit of measure, that ratio is called a rate. For example, a 5°C rise in temerature per hour is a rate and can be expressed as 5 degrees/1 hour or 5°C/hr. Proportions are often used to solve problems involving ratios. You can use the means-extremes property of proportionas to solve equations that have the form of a proportion.
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Let's Practice: Solve each proportion.
| 1. 0.1 2 = 0.5 x
10 |
2.
x+1
4
=
3
4
2 |
3.
4
6
=
8
x
12 |
4.
x
21
=
3
36
1 |
|
5.
9
y+1
=
18
54
26 |
6.
3−x
4+x
=
8
48
2 |
7.
4x
25
=
85−x
100
5 |
8.
x+8
−3
=
17−x
−2
7 |
Use a proportion to solve each problem.
9. To make a model of the Guadelupe River bed, Hermie used 1 inch of clay for 5 miles of the actual river's length. His model river was 50 inches long. How mong is the Guadelupe River?
250 miles 10. Josh finished 24 math problems in one hour. At that rate, how many hours will it take him to complete 72 problems?
3 hours |