1 3 1 2 3 4 Adding and

1. 3 1. 2. 3. 4. Adding and Subtracting Real Numbers; Properties of Real Numbers Add integers. Add rational numbers. Find the additive inverse of a number. Subtract rational numbers.

Adding Fractions with the Same Denominator • Add the numerators. • Keep the same denominator • Simplify.

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. LCD: 12

Adding Fractions ∙ 4 ∙ 1 LCD: 20

Adding Fractions ∙ 2 ∙ 3 LCD: 18

Adding Fractions ∙ 5 ∙ 3 LCD: 18 = 2∙ 3∙ 3 30 = 2∙ 3∙ 5 LCD = 2 ∙ 3 ∙ 5 = 90

Adding Decimals To add decimals: 1. Line up the decimal points. 2. Fill in zeros if necessary. 3. Add columns.

Adding Integers Addends: The numbers being added Sum: the answer 2+3=5 Addends Sum

Adding Integers Properties of Addition Additive Identity Commutative Property of Addition Associative Property of Addition Symbolic Form Word Form Example a+0=a The sum of a number and 0 is that number. 4+0=4 a+b=b+a Changing the order of addends does not affect the sum. 3+5=5+3 (a + b) + c = a + (b + c) Changing the grouping of three or more addends does not affect the sum. (2 + 3) + 4 = 9 2 + (3 + 4) = 9

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 35 + (– 17) Different = subtract, sign of larger = 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 Different = subtract, sign of larger Same = add, keep sign

Adding Rational Numbers ∙ 2 LCD: ∙ 3 12 Different = subtract, sign of larger ∙ 5 LCD: 40 Same = add, keep sign ∙ 4

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 +7 + (-3) = 4 +3 – +5 = – 2 +3 + (-5) = – 2

Subtracting Integers +5 – (-3) = +8 +5 + (+3) = +8 -3 – (-4) = +1 -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 LCD: 8 ∙ 2

Subtracting Decimals 4. 07 – 9. 3 = 4. 07 + (– 9. 3) 2 1 = – 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

Subtract a) b) c) d) Copyright © 2011 Pearson Education, Inc. Slide 1 - 26

Subtract a) b) c) d) Copyright © 2011 Pearson Education, Inc. Slide 1 - 27