Beginning Algebra, 11th Edition

Adding Mentally

Check each answer by adding mentally. If necessary, use a number line.

(a) (b)

(c)

Find a common denominator.

(d)

(e) (f ) (g)

Notice in parts ( f ) and (g) thatwhen additive inverses are added, the sum is 0.

NOW TRY

The rules for adding signed numbers are summarized as follows.

- 4.6+8.1=3.5 - 16 + 16 = 0 42 + 1 - 422 = 0

5

6

+ a- 1

1

3

b =

5

6

+ a-

4

3

b =

5

6

+ a-

8

6

b =-

3

6

=-

1

2

-

1

2

+

1

8

= -

4

8

+

1

8

=-

3

8

7 + 1 - 42 = 3 - 8 + 12 = 4

EXAMPLE 5

SECTION 1.5 Adding and Subtracting Real Numbers 39

Adding Signed Numbers

Same sign Add the absolute values of the numbers. The sum has the same sign

as the given numbers being added.

Different signs Find the absolute values of the numbers and subtract the lesser

absolute value from the greater. Give the answer the same sign as the number

having the greater absolute value.

OBJECTIVE 3 Use the definition of subtraction.Recall that the answer to a

subtraction problem is called a difference.In the subtraction xis called the

minuendand yis called the subtrahend.

To illustrate subtracting 4 from 7, written with a number line, we begin at

0 and draw an arrow 7 units to the right. See FIGURE 15. From the right end of this

arrow, we draw an arrow 4 units to the left. The number at the end of the second arrow

shows that 7- 4 =3.

7 - 4,

x-y,

NOW TRY
EXERCISE 5
Check each answer.

(a)

(b)3.7+ 1 - 5.7 2 =- 2

2

3

+ a- 2

1

9

b=- 1

4

9

NOW TRY ANSWER

5. Both are correct.

–1 1 2 3 4 5 6 7

7

–4

0

7  4  3

FIGURE 15

The procedure used to find the difference is exactly the same procedure

that would be used to find the sum so

This equation suggests that subtractinga positive number from a greater positive

number is the same as addingthe additive inverse of the lesser number to the greater.

This result leads to the definition of subtraction for all real numbers.

7 - 4 = 7 + 1 - 42.

7 + 1 - 42 ,

7 - 4