Ratios compare two sets of numbers and can be written in three ways: using "to", with a colon, or as a fraction. Proportions are two equal ratios where the cross products are also equal. To solve a proportion, cross multiply, divide both sides by the number connected to the variable, and check that it makes a true proportion.

2. RATIOS
Ratios are comparisons made between two sets
of numbers.
For example:
There are eight girls and seven boys in a class.
The ratio of girls to boys is 8 to 7.

3. THERE ARE 3 WAYS TO WRITE RATIOS.
1. Write the ratio using the word “to” between the two
numbers being compared.
For example: There are 8 girls and 5 boys in my class.
What is the ratio of girls to boys?
The ratio is: 8 girls to 5 boys
8 to 5

4. 2. Write a ratio using a colon between the two
numbers being compared.
For example: There are 3 apples and 4 oranges in the
basket. What is the ratio of apples to oranges?
The ratio is: 3 apples to 4 oranges.
3 : 4

5. 3. Write a ratio as a fraction.
For example:
Hunter and Brandon were playing basketball. Brandon
scored 5 baskets and Hunter scored 6 baskets. What
was the ratio of baskets Hunter scored to the baskets
Brandon scored?
The ratio of baskets scored was:
6 baskets to 5 baskets
6
5

6. GUIDED PRACTICE:
Directions: Write the ratio in three different ways.
There are 13 boys and 17 girls in sixth grade.
Find the ratio of boys to the girls in sixth grade.
13 to 17
13
17
13 : 17

7. PROPORTIONS
Proportions are two ratios of equal value.
1 girl
4 boys
4 girls
16 boys
Are these ratios saying the same thing?

8. DETERMINING TRUE PROPORTIONS:
To determine a proportion true, cross multiply.
If the cross products are equal, then it is a true proportion.
4
5
20
25
=
4 x 25
100
20 x 5
100
=
=
The cross products were equal, therefore 4 And 20 makes a true proportion.
5 25

9. Guided Practice:
Directions: Solve to see if each problem is a true proportion.
3
=
15
5 25
1.
2. 6 = 57
8 76
3.
12
7 = 37
60

10. Directions: Solve to see if each problem is a true proportion.
Guided Practice:
3
=
15
5 25
1. 2.
6
8
=
57
76
3. 7
12
= 37
60
15 x 5 = 3 x 25
75 = 75
true
57 x 8 = 6 x 76
456 = 456
true
7 x 60 = 37 x 12
420 = 444
false

11. SOLVING THE PROPORTION:
When solving proportions, follow these rules:
1. Cross multiply.
2.Divide BOTH sides by the number connected to the variable. 3.
Check the answer to see if it makes a true proportion.
Problem:
Which number is
connected to the variable?
Since the 4 is connected
to the variable, DIVIDE
both sides by the 4.
4 ÷ 4 = 1;
therefore you
are left with “n”
on one side.
=
52 n
4 7
4 x n = 52 x 7
4n = 364
4 4
n = 91 miles
364 ÷ 4 = 91