Study Guide and Intervention (continued) - MathnMind

3-6
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Study Guide and Intervention
Ratios and Proportions
Ratios and Proportions A ratio is a comparison of two numbers by division. The ratio
x
of x to y can be expressed as x to y, x:y or . Ratios are usually expressed in simplest form.
y
An equation stating that two ratios are equal is called a proportion.To determine whether
two ratios form a proportion, express both ratios in simplest form or check cross products.
Example 1 Determine whether the Example 2
Use cross products to
24 12
ratios and form a proportion.
36 18
24 2
when expressed in simplest form.
36 3
12 2
when expressed in simplest form.
18 3
10 25
determine whether and form a
18 45
proportion.
10 25
Write the proportion.
18 45
10(45) 18(25) Cross products
24 12
The ratios and form a proportion
36 18
because they are equal when expressed in
simplest form.
450 450 Simplify.
10 25
The cross products are equal, so . 18 45
Since the ratios are equal, they form a
proportion.
Exercises
Use cross products to determine whether each pair of ratios forms a proportion.
1 16
5 10
10 25
1. , 2. , 3. ,
2
32
8 15
20 49
25 15
12 3
4 12
4. , 5. , 6. ,
36 20
32 16
9 27
0.1 5
15 9
14 20
7. , 8. , 9. ,
2 100
20 12
21 30
72 9
10. 2:3, 20:30 11. 5 to 9, 25 to 45 12. ,
64 8
13. 5:5, 30:20 14. 18 to 24, 50 to 75 15. 100:75, 44:33
16. , 17. , 18. , 0.45
0.05 1
1.5 6
0.1
1 20
2 8
0.2 0.9
© Glencoe/McGraw-Hill 167 Glencoe Algebra 1
Lesson 3-6