Adding and Subtracting Real Numbers;
1.3 Properties of Real Numbers
1. Add integers.
2. Add rational numbers.
3. Find the additive inverse of a number.
4. Subtract rational numbers.
Adding Fractions
Adding Fractions with the Same Denominator
• Add the numerators.
• Keep the same denominator
• Simplify.
2 4 2+4 6 2
+ = = =
9 9 9 9 3
Adding Fractions
To add fractions with different denominators:
1. Write each fraction as an equivalent fraction with
the LCD.
2. Add the numerators and keep the LCD.
3. Simplify.
1 1 1( 4 ) 1(3)
+ = +
3 4 3 ( 4 ) 4(3)
4 3
LCD: 12 = +
12 12
7
=
12
Adding Fractions
∙4 ∙1
3 3 12 3
+ = +
5∙ 4 20 ∙ 1 20 20
15
LCD: 20 =
20
3
=
4
Adding Fractions
∙2 ∙3
2 5 4 15
+ = +
9∙ 2 6 ∙3 18 18
LCD: 18
19
=
18
Adding Fractions
∙5 ∙3
7 5 35 15
+ = +
18∙ 5 30∙ 3 90 90
LCD:
50
18 = 2∙3∙3
=
30 = 2∙3∙5 90
LCD = 2 ∙3 ∙3 ∙5
5
= 90
=
9
Adding Decimals
To add decimals:
1. Line up the decimal points.
2. Fill in zeros if necessary.
3. Add columns.
2.4 + .35 2.4 0
.35
2.75
Adding Integers
Addends: The numbers being added
Sum: the answer
2+3=5
Addends Sum
Adding Integers
Properties Symbolic Form Word Form Example
of Addition
Additive a+0=a
The sum of a number
4+0=4
Identity and 0 is that number.
Commutative Changing the order
Property of a+b=b+a of addends does not 3+5=5+3
Addition affect the sum.
Changing the
Associative (2 + 3) + 4 = 9
(a + b) + c = grouping of three or
Property of
a + (b + c) more addends does 2 + (3 + 4) = 9
Addition not affect the sum.
Adding Integers
Adding Numbers with the Same Sign
Procedure:
To add two numbers that have the same sign, add
their absolute values and keep the same sign.
Adding Integers
Adding Numbers with Different Signs
Sign?
Number?
Procedure:
To add two numbers that have different signs,
subtract their absolute values and keep the sign
of the number with the largest absolute value.
Adding Integers
–29 + 7 Different = subtract, sign of larger = –22
Different = subtract, sign of larger
35 + (–17) = 18
–16 + (– 22) Same = add, keep sign
= –38
15 + (–27) Different = subtract, sign of larger = –12
32 + 6 Same = add, keep sign = 38
Adding Rational Numbers
7 � 3� 4
+�- � =
10 � 10 � 10
Different = subtract, sign
of larger 2
=
5
4 � 5� 9 -9
- +� - � =- =
12 � 12 � 12 12
3
Same = add, keep sign
=-
4
Adding Rational Numbers
∙2 ∙3
5 3 - 10 9
- + = +
6 4 12 12
LCD: 12
1
Different = subtract, sign =-
of larger 12
∙5 ∙4
7 9 = - 35 + - 36
- + -
8 10 40 40
40 71
LCD:
=-
Same = add, keep sign 40
Additive inverses: Two numbers whose sum is 0.
Number Additive Inverse
8 -8
-3 3
0 0
Subtracting Integers
5–3=2 Subtracting is the same adding
the additive inverse (the
opposite).
5 + –3 = 2
Procedure:
Rewrite as an addition problem and change the
sign of the number that comes after the operation.
Subtracting Integers
+7 – +3 = +4 +3 – +5 = –2
+7 + (-3) = 4 +3 + (-5) = – 2
Subtracting Integers
+5 – (-3) = +8 -3 – (-4) = +1
+5 + (+3) = +8 -3 + (+4) = +1
Subtracting Integers
–17 – (–4) = –17 + (+4) = –13
8 – 20 = 8 + (-20) = –12
–7 – 15 = –7 + (-15) = –22
14 – 2 = 12
Subtracting Rational Numbers
∙1 ∙2
3 1
- - -3 2
= -
8 4 8 8
LCD: 8
-3 -2
= +
8 8
5
=-
8
Subtracting Decimals
4.07 – 9.3 = 4.07 + (– 9.3) = – 5.23
2
9.310
4.07
5.23
Add – 6 + (–9).
a) –15
b) -3
c) 3
d) 15
Copyright © 2011 Pearson Education, Inc. Slide 1- 22
Add – 6 + (–9).
a) –15
b) -3
c) 3
d) 15
Copyright © 2011 Pearson Education, Inc. Slide 1- 23
Subtract 5 – (–8).
a) –13
b) -3
c) 3
d) 13
Copyright © 2011 Pearson Education, Inc. Slide 1- 24
Subtract 5 – (–8).
a) –13
b) -3
c) 3
d) 13
Copyright © 2011 Pearson Education, Inc. Slide 1- 25
3 �1 �
Subtract - -� �.
7 �3 �
16
a) -
21
1
b) -
2
c) 2
-
21
d) 2
21
Copyright © 2011 Pearson Education, Inc. Slide 1- 26
3 �1 �
Subtract - -� �.
7 �3 �
16
a) -
21
1
b) -
2
c) 2
-
21
d) 2
21
Copyright © 2011 Pearson Education, Inc. Slide 1- 27
