Basic Mathematics for College Students

Solve application problems by using the order

of operations rule.

Sometimes more than one operation is needed to solve a problem.

2

286 Chapter 3 Fractions and Mixed Numbers

Solution

The key word differenceindicates subtraction. Since we are to add to the

difference, the difference should be written first within parentheses, followed by the

addition.

to

Translate from words to numbers and mathematical symbols.

Prepare to add the fractions. Build so that its

denominator is 12:.

Add the numerators of the fractions: 7 4 11.

 (^7) Write the sum over the common denominator 12.

11

12

1

3 

4

4 

4

12

1

^73

12

 7

4

12

Subtract the numerators: 10 3 7.

Write the difference over the common

denominator 12.



7

12

 7

1

3

Multiply the numerators.

b (^7) Multiply the denominators.

1

3

10

12



3

12

a

Prepare to subtract the fractions

within the parentheses. Build the

fractions so that their denominators

are the LCD 12.

b 7

1

3

5

6



2

2



1

4



3

3

b 7

1

3

a

5

6



1

4

a

a

5

6



1

4

b 7

1

3

 

the difference of

5

6

and

1

4

Add 7.

1

3

(^7 13)
Self Check 4
MASONRYFind the height of a
wall if 8 layers (called courses)
of -inch-high blocks are held
together by -inch-thick layers
of mortar.
Now TryProblem 77
1
4

7 38

EXAMPLE (^4) Masonry To build a
wall, a mason will use blocks that are inches
high, held together with -inch-thick layers of
mortar. If the plans call for 8 layers, called
courses,of blocks, what will be the height of the
wall when completed?
Analyze

• The blocks are inches high. Given


• A layer of mortar is inch thick. Given


• There are 8 layers (courses) of blocks. Given


• What is the height of the wall when completed? Find
  Form To find the height of the wall when it is completed, we could add the heights
  of 8 blocks and 8 layers of mortar. However, it will be simpler if we find the height
  of one block and one layer of mortar, and multiply that result by 8.

is equal to times plus

=8 b

3

8

5 

3

4

a

The height of

the wall when

completed

¢

the thickness

of one layer

of mortar.

the height

of one

block

8 °

The height of

the wall when

completed

3

8

5 43

3

8

(^5 34)
(^3) –
Blocks 5 4 in. high
(^3) –
8
Mortar in. thick