# 2-5 Ratios and Proportions Homework

```NAME ______________________________________________ DATE______________ PERIOD _____
2-6
Homework
Study
Guide and Intervention
Solve Proportions
If a proportion involves a variable, you can use cross products to solve
x
10
the proportion. In the proportion !! &quot; !!, x and 13 are called extremes. They are the first
5
13
and last terms of the proportion. 5 and 10 are called means. They are the middle terms of the
proportion. In a proportion, the product of the extremes is equal to the product of the means.
Means-Extremes Property of Proportions
x
5
Example
a
b
c
d
For any numbers a, b, c, and d, if ! &quot; ! , then ad &quot; bc.
10
13
Solve &quot; ! &quot; .
x
10
Use cross
products
to determine whether each pair of ratios forms a proportion
Original proportion
!&quot;!
5
13
13(x) &quot; 5(10)
1.13x
2:3,&quot;14:21
50
13x
50
!&quot;!
13
13
11
x &quot; 3!
13
Cross products
2. 5 to 9, 25 to 45
Simplify.
Divide each side by 13.
Simplify.
Exercises
Solve each proportion. Show the steps
\$3
x
2
8
Copyright &copy; Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3
63
4
6
8
x
6. ! &quot; !
3
d
18
3
9. ! &quot; !
5. ! &quot; !
9
y#1
18
54
8. ! &quot; !
10. ! &quot; !
4
b\$2
4
12
11. ! &quot; !
a\$8
12
15
3
14. ! &quot; !
13. ! &quot; !
x
21
3. ! &quot; !
3
4
7. ! &quot; !
0.5
x
5
3
x#1
4
4. ! &quot; !
0.1
2
1
t
2. ! &quot; !
1. ! &quot; !
5
8
p
24
1.5
x
12
x
12. ! &quot; !
12
k
24
k
15. ! &quot; !
3#y
4
\$y
8
2#w
6
12
9
Use a proportion to solve each problem.
16. MODELS To make a model of the Guadeloupe River bed, Hermie used 1 inch of clay for
5 miles of the river’s actual length. His model river was 50 inches long. How long is the