Basic Mathematics for College Students

Chapter 5 Summary and Review 481

When we compare two quantities that have
different units (and neither unit can be
converted to the other), we call the comparison
a rate.

To write a rate as a fraction,write the first
quantity mentioned as the numerator and the
second quantity mentioned as the
denominator, and then simplify, if possible.
Write the units as part of the fraction.

Words such as per, for, in, from,and onare used
to separate the two quantities that are
compared in a rate.

Write the rate 33 miles in 6 hoursas a fraction in simplest form.

33 miles in6 hours can be written as

Write the units as part of the rate.

The rate can be written as 11 miles per 2 hours.



11 miles

2 hours

To simplify, factor 33 and 6. Then

remove the common factor of 3 from

the numerator and denominator.

33 miles

6 hours



3

1

11 miles

2  3

1

hours



33 miles

6 hours



A unit rateis a rate in which the denominator
is 1.

To write a rate as a unit rate, divide the
numerator of the rate by the denominator.

A slash mark/ is often used to write a unit rate.

Write as a unit rate: 2,490 apples from 6 trees.

To find the unit rate, divide 2,490 by 6.

The unit rate is. This rate can also be expressed as: ,

415 apples per tree, or 415 apples/tree.

(^4151) treeapples 415 applestree

415

6 2,490

A unit priceis a rate that tells how much is paid
for oneunit (or oneitem). It is the quotient of
price to the number of units.

Unit price 

Comparison shopping can be made easier by
finding unit prices.The best buy is the item that
has the lowest unit price.

price

number of units

Which is the better buy for shampoo?

12 ounces for $3.84 or 16 ounces for $4.64

To find the unit price of a bottle of shampoo, write the quotient of its

price and its weight, and then perform the indicated division. Before

dividing, convert each price from dollars to cents so that the unit price

can be expressed in cents per ounce.

One ounce of shampoo for 29¢ is better than one ounce for 32¢. Thus,

the 16-ounce bottle is the better buy.

32¢ per oz 29¢ per oz

$4.64

16 oz



464¢

16 oz

$3.84

12 oz



384¢

12 oz

Write each ratio as a fraction in simplest form.

1. 7 to 25 2. 15  16


2. 24 to 36 4. 21  14


3. 4 inches to 12 inches 6. 63 meters to 72 meters


4. 0.28 to 0.35 8. 5.11.7


5. 
   
   
   
   10. 
       
   
   
   
   


6. 15 minutes : 3 hours 12. 8 ounces to 2 pounds

4

1

6

 3

1

3

2

1

3

to 2

2

3

Write each rate as a fraction in simplest form.

13. 64 centimeters in 12 years


14. $15 for 25 minutes

Write each rate as a unit rate.

15. 600 tickets in 20 minutes


16. 45 inches every 3 turns


17. 195 feet in 6 rolls


18. 48 calories in 15 pieces

REVIEW EXERCISES