ratios and proportions
DESCRIPTION
Ratios and Proportions. Objective I will solve proportions using reciprocals and cross products. I will use proportions to solve real-life problems. Vocabulary. Proportion - an equation in which one ratio is set equal to another ratio - PowerPoint PPT PresentationTRANSCRIPT
Ratios and Proportions
Objective
• I will solve proportions using reciprocals and cross products.
• I will use proportions to solve real-life problems.
Vocabulary1. Proportion - an equation in which one
ratio is set equal to another ratio
(Written in the form of , which is read as “a is to b, as c is to d”)
a
bc
d
Using the Reciprocal PropertySolve the proportion .SOLUTION
4
y8
3
y
43
8
y 4 •3
8
y 12
8
y 3
2
4
y8
3
Write original proportion
Use reciprocal property
Multiply each side by 4
Simplify
Using the Reciprocal Property
Solve the proportion .
CHECK
Substitute
4
y8
3
4
3/24 •
2
38
3
Using the Cross Product Property
Solve the proportion .
x
416
x
x
416
xx • x 4 •16
x 2 64x 8
Write original proportion
Use cross product property
Simplify
Take square root of both sides
The solutions are x=-8 and x=8. Check both answers.
Checking SolutionsSolve the proportion.
x 2 16x 4
x 42
2(x 2 16)(x 4)(x 4)
2x 2 32x 2 16
x 2 16x 4
Use cross product property
Use distributive property
Isolate variable term
Take square root of both sides
Checking SolutionsCheck each solution.
x = 4: x = -4
x 2 16x 4
x 42
42 164 4
4 42
0
80
2
00
x 2 16x 4
x 42
( 4)2 16 4 4
4 42
0
0
82
The solution x = -4 is extraneous because the check results in a false statement. The correct solution is x = 4.
Proportions in Real-LifeArchaeologists excavated three pits containing the
clay army. To estimate the number of warriors in Pit 1 shown below, an archaeologist might excavate three sites. The sites at the ends together contain 450 warriors. The site in the central region contains 282 warriors. This 10-meter-wide site is thought to be representative of the 200-meter central region. Estimate the number of warriors in the central region. Then estimate the total number of warriors in Pit 1.
Proportions in Real-Life
Central Region 200m
282 warriors
240 warriors
10m
5m 5m
210 warriors
62m
SOLUTION Let n represent the number of warriors in the 200-meter central region. You can find the value of n by solving a proportion.
Number of warriors found Number of meters excavated
=
Total number of warriors Total number of meters
282 = 10
n 200
Proportions in Real-Life
The solution is n = 5640, indicating that there are about 5640 warriors in the central region. With the 450 warriors at the ends, that makes a total of about 6090 warriors in Pit 1.
Practice
1.16
412
x
2.5
8x
9
3.x 3x
x
x 6