Download Ratios and Proportions

3.1
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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  5 x
5
x
5
24
5
1. Calculate the cross products.
2. Set the cross products equal.
3. Solve the equation.
Solving Proportions
x  12  12x
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
3x  5
42
x5 7

6
3
3x  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
600x
x
24.80

940
600
23312  600x
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
8
10

x
5
10 x  40
6
10
x4
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