Ratios explained with examples

1. Ratios and Proportions
3.1
1. 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!!

2. 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.

3. A bin at a hardware store contains 120 washers
and 85 bolts. Write the ratio of washers to bolts in
simplest form.
Ratios
The ratio of washers to bolts bolts
washers

85
120

17
24

Express the ratio as a unit ratio. Interpret the answer.
17
24
1
41
1.

There are 1.41 washers for every bolt.

4. The price of a 10.5 ounce can of soup is $1.68. Write
the unit ratio that expresses the price to weight.
Ratios
The ratio of price to weight
weight
price

10.5
1.68

1
16
.

Interpret the answer.
The soup costs $.16 per ounce.

5. 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?
Ratios
The ratio of hydrogen atoms to total atoms
atoms
total
atoms
hydrogen
24
12

2
1


6. Proportions
4
3
8
6

Proportion: two ratios set equal.
24
6
4 
 24
8
3 

Cross-products of proportions are always equal!
Only works if there is an equal (=) sign!
4
3
8
6
 No!

7. Solving Proportions
1. Calculate the cross products.
2. Set the cross products equal to each other.
3. Solve the equation.
8
5
3 x

24
8
3 
 x
x 5
5 

x
5
24 
5
5
5
24

x