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