Basic Mathematics for College Students

Write rates as fractions.

When we compare two quantities that have different
units (and neither unit can be converted to the other), we
call the comparison a rate,and we can write it as a
fraction. For example, on the label of the can of paint
shown on the right, we see that 1 quart of paint is needed
for every 200 square feet to be painted. Writing this as a
rate in fractional form, we have

The Language of Mathematics The word peris associated with the

operation of division, and it means “for each” or “for every.” For example,

when we say 1 quart of paint per200 square feet, we mean 1 quart of paint for

every200 square feet.

Rates

A rateis a quotient of two quantities that have different units.

When writing a rate, always include the units. Some other examples of rates are:

• 16 computers for75 students


• 1,550 feet in4.5 seconds


• 88 tomatoes from3 plants


• 250 miles on2 gallons of gasoline

The Language of Mathematics As seen above, words such as per, for, in,

from,and onare used to separate the two quantities that are compared in a

rate.

Read as “1 quart per

200 square feet.”

1 quart

200 square feet

4

5.1 Ratios 419

Solution
To express 2 pounds in ounces, we use the fact that there are 16 ounces in one
pound.

We can now express the ratio 12 ounces to 2 poundsusing the same units:

12 ouncesto 32 ounces

Next, we write the ratio in fraction form and simplify.

The ratio in simplest form is.

3

8



3

8

To simplify, factor 12 as 3 4 and 32 as 4 8. Then

remove the common factor of 4 and the common units

of ounces from the numerator and denominator.

12 ounces

32 ounces



3  4

1

ounces

4

1

8 ounces

2 16 ounces32 ounces