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 Adding Fractions with the Same Denominator Add the numerators. Keep the same denominator Simplify.
2 4 24 6 2 3 9 9 9 9 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 4 1(3) 1 1 3 4
3 4 4(3) LCD: 12 4 3 12 12 7 12 Adding Fractions 4 1 3 3 5 4 20 1 LCD: 20
12 3 20 20 15 20 3 4 Adding Fractions 2 2 5 9 2 6 LCD: 18
3 3 4 15 18 18 19 18 Adding Fractions 5 3 7 5 35 15
18 5 30 3 90 90 LCD: 18 = 233 30 = 235 LCD = 2 3 3 5 = 90 50 90 5 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
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 7 3 10 10 Different = subtract, sign of larger 4 5
12 12 Same = add, keep sign 4 10 2 5 9 12 3 4 9 12
Adding Rational Numbers 2 3 5 3 6 4 LCD: 9 10 12 12 12
1 12 Different = subtract, sign of larger 5 4 7 9 35 36 40 40 8 10 LCD: 40 Same = add, keep sign
71 40 Additive inverses: Two numbers whose sum is 0. Number Additive Inverse 8 -8 -3 3 0 0
Subtracting Integers 53=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 3 1 8 4 LCD: 8
2 3 2 8 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 Subtract a) 16 21
b) 1 2 c) d) 3 7 1 3 .
2 21 2 21 Copyright 2011 Pearson Education, Inc. Slide 1- 26 Subtract a) 16 21 b)
1 2 c) d) 3 7 1 3 . 2 21
2 21 Copyright 2011 Pearson Education, Inc. Slide 1- 27
