Adding and Subtracting Real Numbers

objectives Add two numbers with the same sign. Add two numbers with different sign. Use the definition of subtraction. Use the rules for order of operations with real numbers. Translate words and phrases involving addition and

subtraction. Use signed numbers to interpret data.

Add the numbers. If both are positive, the sum is positive; if both are negative, the sum is negative.

Objective 1 Add two numbers with the same sign

Add two positive numbers: 3+6=

+3+6

Add two negative numbers: -3 + (-6)=

- 3 - 6

Find the absolute values of the numbers and subtract the lesser absolute value from the grater. Give the answer the same sign as the number having the grater absolute value

Objective 2 Add two numbers with the different sign

+8

–5

Step 1 Draw an arrow from 0 to 8.

Step 2 Then draw a second arrow 5 units to the left to represent adding –5.

Step 3 The second arrow ends at the sum 3.

Answer:

Example 3Use a number line to find .

Find the sum .

Example 3

Find the absolute values of the numbers and subtract the lesser absolute value from the grater. Give the answer the same sign as the number having the grater absolute value.

Objective 2 Add two numbers with the different sign

55

88

358

Find the sum

.

55

1212

7512

The sum will be negative , since

.

The sum will be positive , since

Answer

.

Example 4

Find .

Adding Mentally

Find

Find

Find

Find

Find

Objective 3 Subtracting real numbers

To subtract signed numbers, add the opposite.

(A.T.O.) and use the rules of addition.

6 – (+3) = 6 + (-3) =

6 – (-3) = 6 + (+3) =

-8 – (+2) = -8 + (-2) =

-30 – (-50) = -30 + (+50) =

Mental Math. Find each difference

3412

)33(9

)24(9

45

1012

Objective 4 Use the rules for order of operations with real numbers

𝑎 .−6−[2− (8+3 )]

𝑏 .5+[ (−3−2 )− (4−1 )]

𝑐 . 23−[ 112−(− 14 ) ]

¿23−412

Objective 5 Translate words and phrases involving addition and subtraction

𝑎 . h𝑡 𝑒 𝑠𝑢𝑚𝑜𝑓 −8𝑎𝑛𝑑 4𝑎𝑛𝑑6

𝑏 .3𝑚𝑜𝑟𝑒 h𝑡 𝑎𝑛−5 ,𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒𝑑𝑏𝑦 12

𝑐 . h𝑇 𝑒𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒𝑏𝑒𝑡𝑤𝑒𝑒𝑛−3𝑎𝑛𝑑−8

𝑑 .12𝑠𝑢𝑏𝑡𝑟𝑎𝑐𝑡𝑒𝑑 𝑓𝑟𝑜𝑚18

𝑒 .6 𝑙𝑒𝑠𝑠5

𝑓 .6 𝑙𝑒𝑠𝑠 h𝑡 𝑎𝑛5

g

h .4 𝑙𝑒𝑠𝑠 h𝑡 𝑎𝑛−6

The highest Fahrenheit temperature ever recorded in Barrow, Alaska, was 79°F, while the lowest was −56°F. What is difference between these highest and lowest temperatures? (Source: World Almanac and Book of Facts.)

Solution:

Slide 1.5-25

EXAMPLE 10 Solving a Problem Involving Subtraction

Solution:

Refer to Figure 17 and use a signed number to represent the change in the CPI from 2002 to 2003.

Slide 1.5-27

EXAMPLE 11

Using a Signed Number to Interpret Data

Objective 6 Use signed numbers to interpret data

Multiplying and dividing Real Numbers.

What you’ll l

earn

To find products and quotients of real numbers.

Vocabulary: multiplicative inverse reciprocal

Multiplication of real numbersThe product of two numbers having the same sign is positive.

The product of two numbers having different sign is negative.

15)3)(5(

15)3)(5(

1535

15)3(5

15)3)(5( 15)3(5

15)3)(5( 15)3(5

))((

))((

))((

))((

Multiply Rational Numbers

Multiplying rational numbers is similar to multiplying integers.

Example:

8

3

3

2

24

6

8

3

3

2

8

2

324

36

Simplify by 3

Example:

4

3

3

2

12

6

4

3

3

2

Simplify by 3

4

2

312

36

Simplify by 2

2

1

24

22

Evaluate expressions that contain rational numbers

Evaluate3

2nif

8

52n

Multiplicative property of -1 The product of any number and -1 is its called additive inverse.

For any number a, -1( a ) = a( -1 ) = - a

Example:

Division of real numbers

The quotient of two numbers having the same sign is positive.

The quotient of two numbers having different sign is negative.

12)2(24

12224

12)2(24

)()(

)()(

)()(

)()(

12224 12

2

24

122

24

122

24

122

24

Simplify before dividing

The fraction bar is a grouping symbol

Example: Simplify the expression

)5(7

)812(3

Dividing Rational NumbersThe sign rules for division with integers also apply to division with rational numbers.

Example:4

1

5

2

1

4

5

2

Remember that to divide by any nonzero number, multiply by the reciprocal of that number

Invert the denominator then multiply

c

d

b

a

d

c

b

a

5

31

5

8 or

Dividing Rational Numbers

Example:

83

15

c

d

b

a

d

c

b

a

Evaluate expressions that contain rational numbers

Evaluate2c

ab3,2.5,8.7 cbaif