RATIO AND PROPORTION
RATIOS AND RATES
Quantities such as 8 feet, 16 cents or 10 hours are numerical quantities written with units. A ratio is a
comparison of two quantities with the same units. For example, if we want to compare the heights of
two trees, one 6 feet tall and the other 8 feet tall, we can write this ratio three ways:
1) As a fraction: 6ft
8ft
62
8
== 3
2
•3
4
4
=
•
2) With a colon: 6 ft : 8 ft = 6 : 8 = 3 : 4
3) With the word to: 6 ft to 8 ft. = 6 to 8 = 3 to 4.
Notice that in each case,
• The order of the numbers in a ratio is important! To write a ratio as a fraction, place the first
number of the ratio in the numerator; place the second number in the denominator.
• The ratio is written in lowest terms.
• The units are not written as part of the ratio. Because a ratio compares two quantities with the
same units – convert the units if they are different.
Example 1: Write each ratio as a fraction in lowest terms.
A) 15 pounds to 24 pounds
The units are the same, so we can write this ratio as
15 pounds to 24 pounds = 15 3
24 =5
3
•5
8
8
=
•
B) 75 cents to $1.25
Here, the units are not the same. Since $1 = 100 cents, to convert $1.25 to cents, drop the
dollar sign and move the decimal point two places to the right.
$1.25 = 1.25 = 125 cents
75 cents to $1.25 = 75 cents to 125 cents = 75 3 25
125 =•
525•
3
5
=
A rate is a comparison of two quantities with different units, such as 10 g per 180 mL. Like a ratio, a
rate can be written as a fraction, with a colon, or with the word to. A rate is also expressed in lowest
terms. Unlike a ratio, the units are written as part of the rate. For example, to write the rate “10 g per 180 mL” as a
fraction in lowest terms, cancel the corresponding 0’s and keep the units:
10 g per 180 mL = 10 g
18 0
1 g
18 mL
mL =
PBCC 1 SLC Lake Worth Math Lab
