ratios and proportions. warm up - simplify ratio – comparison of two numbers by division....
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Ratios and Proportions
Warm Up - Simplify
108)a
2
11b
21
3)c
36
2
22
7
21
Ratio – comparison of two numbers by division.
Proportion – an equation stating that two ratios are equal.
Ratio# boys to # girls
# boys : # girls#
#
boys
girls
Ratios are equal if the cross products are equal.
24 4
30 5
120120
430524
:
xx
Check
Solve24
15 16
n
5.2216
360
16
16
36016
)15)(24(1616
24
15
n
n
n
n
n
2
45Or
Solve3 1
5 7
x x
16
7
716
5721
5)13)(7(75
13
x
x
xx
xx
xx
Solve 8 3
4 1 2 5x x
4
37
374
3124016
)14(3)52(852
3
14
8
x
x
xx
xxxx
Seth earns $152 in 4 days. At that rate, how many days will it take him to earn $532?
daysx
x
xx
14
2128152
)532(4152
532
4
152
Lanett drove 248 miles in 4 hours. At that rate, how long did it take her to drive 93 miles?
hoursx
x
xx
x
5.1
1488248
)372(4248
372
4
248
)93(
4
248
A blueprint for a house states that 2.5 inches equals 10 feet. If the length of a wall is 12 feet, how long is the wall on the blueprint?
inchesx
x
x
ft
x
ft
in
3
3010
)12)(5.2(10
12.10
.5.2
The ratio of the measures of the angles of a triangle is 2 :7 : 3. Find the measure of the smallest angle of the triangle.
Smallest Angle:
15
18012
180372
x
x
xxx
30)15(2
2x
The profits in a business are shared by three partners in the ratio 4 : 5 : 9. The profits for the year was $720,000. Determine the number of dollars received by the partner with the second largest share.
Find x:Find the 2nd largest shared holder’s profit:
000,40
000,72018
000,720954
x
x
xxx
000,200$
)000,40(5
5x
The ratio of the measures of the angles of a triangle is 3 : 4 : 2. Find the measure of the largest angle of the triangle.
Find x: The largest angle:
20
1809
180243
x
x
xxx
80
)20(4
4x
If the ratio of boys to girls in a geometry class is 3:1, and there are 28 students in the class, how many are boys?
Find x:Find the number of boys.
7
284
283
x
x
xx
Boys
xBoys
21)7(3
3:
The width of a rectangle is 3/5 of the length. The perimeter is 48 feet. Find the area of the rectangle.
lw5
3
.15
24016
240610
485
62
485
322
22
ftl
l
ll
ll
ll
Pwl
..135
)9(15
155
315
ftsqA
A
A
lxwArea