Transcript Section 3.1
3.1
1.
2.
3.
4.
Ratios and Proportions
Solve problems involving ratios.
Solve for a missing number in a proportion.
Solve proportion problems.
Use proportions to solve for missing lengths in figures
that are similar.
You may use calculators in this chapter!!
Ratio: A comparison of two quantities
using a quotient (fraction).
The word to separates the numerator and
denominator quantities.
12
The ratio of 12 to 17 translates to .
17
Numerator Denominator
Unit ratio: A ratio with a denominator of 1.
Ratios
A bin at a hardware store contains 120 washers
and 85 bolts. Write the ratio of washers to bolts in
simplest form.
The ratio of washers to bolts
washers
bolts
24
120
17
85
Express the ratio as a unit ratio. Interpret the answer.
1.41
24
1
17
There are 1.41 washers for every bolt.
Ratios
The price of a 10.5 ounce can of soup is $1.68. Write
the unit ratio that expresses the price to weight.
The ratio of price to weight
price
weight
Interpret the answer.
The soup costs $.16 per ounce.
.16
1.68
1
10.5
Ratios
One molecule of glucose contains 6 carbon atoms, 12
hydrogen atoms, and 6 oxygen atoms. What is the
ratio of hydrogen atoms to the total number of atoms
in the molecule?
The ratio of hydrogen atoms to total atoms
hydrogen atoms
12
total atoms
24
1
2
Proportions
Proportion: two ratios set equal.
4 6 24
3 8 24
6 3
8 4
Cross-products of proportions are always equal!
Only works if there is an equal (=) sign!
6 3
8 4
No!
Solving Proportions
1. Calculate the cross products.
2. Set the cross products equal to each other.
3. Solve the equation.
3 8 24
5 x 5x
3 x
5 8
24 5x
5
x
5
24
5
1. Calculate the cross products.
2. Set the cross products equal.
3. Solve the equation.
Solving Proportions
x 12 12 x
20 18 360
12 18
20
x
12x 360
12
12
x 30
1. Calculate the cross products.
2. Set the cross products equal.
3. Solve the equation.
Solving Proportions
2
m
5
3
69
4 1 7 2 9 23
2
2
2 2 3 2 31
7
5 3
1 m
4
2
Multiply by reciprocal.
1 1
5 22 569 69
mm
21 55 22 2
1
345
m
4
1
86
4
Or clear the fraction.
2
69
10 m 10
5
2
1. Calculate the cross products.
2. Set the cross products equal.
3. Solve the equation.
Solving Proportions
3x 5
42
x5 7
6
3
3x 5 42
3x 15 42
15 15
3x 27
3
x 9
3
Solving Proportions
Gary notices that his water bill was $24.80 for 600
cubic feet of water. At that rate, what would the
charges be for 940 cubic feet of water?
dollars
cubic feet
23312
600 x
x
24.80
940
600
23312 600 x
600
600
x $38.85
Solving Proportions
Chevrolet estimates that its 2012 Tahoe will travel
520 miles on one tank of gas. If the tank of the
Tahoe holds 26 gallons, how far can a driver expect
to travel on 20 gallons?
miles
gallon
10400
26 x
520
26
x
20
10400 26 x
26
26
x 400 miles
Congruent angles: Angles that have the same measure.
The symbol for congruent is .
Similar figures: Figures with congruent angles and
proportional side lengths.
The two figures are similar. Find the missing length.
40
10 x
8
10
x
5
large
small
10
5
8
x
10 x 40
6
10
x4
10
Similar Figures
The two figures are similar. Find the missing lengths.
Round your answer to the nearest hundredth.
6.5x
134.4
x
x
12.8
6.5 10.5
12.8 km
large
small
y
134.4 6.5x
6.5
6.5
x 20.68 km
10.5 km
6.5y
58.88
6.5 km
6.5 km
4.6 km
y
12.8
6.5 4.6
58.88 6.5y
6.5
6.5
y 9.06 km