Basic Mathematics for College Students

278 Chapter 3 Fractions and Mixed Numbers

“Americans are not getting the

sleep they need which may affect

their ability to perform well

during the workday.”

National Sleep Foundation Report, 2008

The 1,000 people who took part

in the 2008 Sleep in Americapoll

were asked when they typically

wake up, when they go to bed,

and how long they sleep on both

workdays and non-workdays.

The results are shown on the

right. Write the average hours

slept on a workday and on a non-

workday as mixed numbers. How

much longer does the average

person sleep on a non-workday?

THINK IT THROUGH

Typical Workday and Non-workday Sleep Schedules

Average non-workday

bedtime

11:24 PM

Average hours

slept on

non-workdays

7 hours

25 minutes

7:12 AM

Average non-workday

wake time

Average workday

bedtime

10:53 PM

Average hours

slept on workdays

6 hours

40 minutes

5:35 AM

Average workday

wake time

(Source: National Sleep Foundation, 2008)

Form The key phrase combined lengthindicates addition.

We translate the words of the problem to numbers and symbols.

is equal to plus plus



SolveTo find the sum, we will write the mixed numbers in vertical form. To add in

the fraction column, the LCD for , , and is 16.

Build and so that their denominators are 16.

Add the fractions separately.

Add the whole numbers

separately.

StateThe combined length of the three races of the Triple Crown is miles.

CheckWe can estimate to check the result. If we round down to 1, round

down to 1, and round up to 2, the approximate combined length of the three

races is 1  1  2 4 miles. Since 3 1516 is close to 4, the result seems reasonable.

(^112)

114 1 163

(^3 1516)

1

4

16

1

3

16

 1

8

16

3

15

16

1

4

16



1

3

16



 1

8

16



15

16

1

1

4



4

4



1

3

16



 1

1

2



8

8



1

1

4



1

3

16



 1

1

2



  

1

2

1

4

1

2

3

16

1

4

1

1

2

1

3

16

1

1

4

The combined

length of the

three races

the length

of the

Belmont

Stakes.

the length

of the

Preakness

Stakes

the length

of the

Kentucky

Derby

The combined

length of the

three races