Download M-30 2 pg 1 Ratios.cwk (WP)

Chapter 2
Ratios and Proportions
Page 1
Ratios
A Ratio is a comparison of two quantities that both have the same unit of measure. A ratio can be
expressed in 3 different ways: in words, with a colon or as a fraction. When we use words to
express the 2 quantities we state the first number and then use the word “to” and then state the
second number. When we use a colon we replace the word “to” with a colon. When we express the
ratio in fraction form we put the first number given in the numerator (top) of the fraction and the
second number given in the denominator (bottom) of the fraction. In all three forms we state the
ratio without the common unit. We do not convert the fraction into a mixed number.
Example 1
We want to compare 5 feet to 12 feet. This comparison can be written as a ratio in 3 ways.
In words: 5 to 12
Using a colon: 5 : 12
As a fraction:
5
12
Example 2
We want to compare 8 days to 3 days. This comparison can be written as a ratio in 3 ways.
In words: 8 to 3
Using a colon: 8 : 3
As a fraction:
8
3
Simplifying a Ratio
A ratio is in simplest form when the fraction has been reduced and the units have been canceled out.
We do not convert the fraction into a mixed number.
Example 3
12 miles to 15 miles
12 miles 1/ 2/ 4 m
/ /i/le/ /s 4
= 5
=
15 miles 1/ 5/ m
/ /i/le/ s/ 5
Example 4
36 cars to 14 cars
36 cars 3/ 6/ 18 c/ a/ /r/s 18
=
=
14 cars 1/ 4/ 7 c/ a/ r/s/
7
We write ratios as a fraction with whole numbers. Move the decimal in the numerator and the
denominator the same number of places to the right to ensure that you have whole numbers.
Example 5
2.4 ounces. to 3.6 ounces
move the decimal one place each
2.4 ounces 24 o/ u/ n/ c/ e/ s/ 2/ 4/ 2
2
=
= 3 =
3.6 ounces 36 o/ u/ n/ c/ e/ s/ 3/ 6/
3
Chapter 2
Example 6
.88 yards to 1.6 yards
move the decimal two places
.88 yards 88 y/ a/ /rd/ /s
8/ 8/ 11
11
=
=
=
20
1.6 yards 160 y/ a/ r/d/ s/ 1/ 6/ 0/
20
© 2015 Eitel
Writing Ratios
Write each ratio with a colon. Do not state the common unit.
1. 16 to 5
2. 8 feet to 11 feet
3. 12 days to 5 days
Write each ratio as a fraction. Do not state the common unit.
4. 5 to 16
5. 13 miles to 4 miles
6. $ 40 to $ 13
Simplifying Ratios
Write each comparison as a ratio in fraction in simplest form.
7. 16 to 12
8.
14 to 8
9.
1.20 to
.76
Page 2 answers
1. 16 : 5
4
3
Chapter 2
7.
2. 8 : 11
8.
7
4
3. 12 : 5
9.
30
19
4.
5
16
5.
13
4
6.
40
13
© 2015 Eitel
Chapter 2
© 2015 Eitel