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Ratios and Proportions3.13.11. Solve problems involving ratios.2. Solve for a missing number in a proportion.3. Solve proportion problems.4. 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.
The ratio of 12 to 17 translates to 12
17.
Numerator Denominator
Unit ratio: A ratio with a denominator of 1.
A bin at a hardware store contains 120 washers and 85 bolts. Write the ratio of washers to bolts in simplest form.
RatiosRatios
The ratio of washers to bolts boltswashers
85
120
1724
Express the ratio as a unit ratio. Interpret the answer.
1724
1411.
There are 1.41 washers for every bolt.
The price of a 10.5 ounce can of soup is $1.68. Write the unit ratio that expresses the price to weight.
RatiosRatios
The ratio of price to weight weightprice
10.51.68
116.
Interpret the answer.
The soup costs $.16 per ounce.
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?
RatiosRatios
The ratio of hydrogen atoms to total atoms
atoms totalatoms hydrogen
2412
21
ProportionsProportions
43
86
Proportion: two ratios set equal.
2464 2483
Cross-products of proportions are always equal!
Only works if there is an equal (=) sign!
43
86
No!
Solving ProportionsSolving Proportions
1. Calculate the cross products.2. Set the cross products equal to each other.3. Solve the equation.
853 x
2483 xx 55
x524 55
524
x
Solving ProportionsSolving Proportions
x18
2012
xx 1212 3601820
36012 x1212
30x
1. Calculate the cross products.2. Set the cross products equal.3. Solve the equation.
Solving ProportionsSolving Proportions
m32
7
21
4
52
m52
32
721
4
269
52
m
4345
m
1. Calculate the cross products.2. Set the cross products equal.3. Solve the equation.
323
29
269
269
1052
10 m
269
25
52
25
m1
1
1
1
3
1
41
86
Multiply by reciprocal. Or clear the fraction.
Solving ProportionsSolving Proportions
37
65
x
53 x 42
4253 x
33
9x
1. Calculate the cross products.2. Set the cross products equal.3. Solve the equation.
42153 x1515
273 x
Solving ProportionsSolving Proportions
Gary notices that his water bill was $24.80 for 600 cubic feet of water. At that rate, what would the charges be for 940 cubic feet of water?
feet cubicdollars
600
8024.
23312 x600
x60023312 600600
8538.$x
940x
Solving ProportionsSolving 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?
gallonmiles
26
520
10400 x26
x2610400 2626
miles 400x
20x
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.
108
6
5x
smalllarge
510
x10 40
4010 x1010
4x
x8
Similar FiguresSimilar FiguresThe two figures are similar. Find the missing lengths. Round your answer to the nearest hundredth.
smalllarge
56812..
4134. x.56
x.. 564134 5656 ..
km 6820.x
510.x
12.8 km
10.5 km
6.5 km 6.5 km
4.6 km
x
y
56812..
8858. y.56
y.. 568858 5656 ..km 069.y
64.y
