Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Fraction Notation: Addition, Subtraction, and Mixed Numerals 4 4.1 Least Common Multiples 4.2 Addition, Order, and Applications 4.3 Subtraction, Equations, and Applications 4.4 Solving Equations: Using the Principles Together 4.5 Mixed Numerals 4.6 Addition and Subtraction of Mixed Numerals; Applications 4.7 Multiplication and Division of Mixed Numerals; Applications 4.8 Order of Operations and Complex Fractions Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 2

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications a Add using fraction notation when denominators are the same. b different. c Use < or > to form a true statement with fraction notation. d Solve problems involving addition with fraction notation. b Simplify fraction notation like n/n to 1, 0/n to 0, and n /1 to n. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 3

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications a Add using fraction notation when denominators are the same. Addition using fraction notation corresponds to combining or putting like things together, just as when we combined like terms. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 4

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications To add when denominators are the same, a) add the numerators, b) keep the denominator, and c) simplify, if possible. a Add using fraction notation when denominators are the same. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 5

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications a Add using fraction notation when denominators are the same. Add and, if possible, simplify. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 6

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications a Add using fraction notation when denominators are the same. We may need to add fractions when combining like terms. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 7

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications a Add using fraction notation when denominators are the same. 5 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 8

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications b Add using fraction notation when denominators are different. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 9

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications To add when denominators are different: a) Find the least common multiple of the denominators. That number is the least common denominator, LCD. b) Multiply by 1, writing 1 in the form of n/n, to find an equivalent sum in which the LCD appears in each fraction. c) Add the numerators, keeping the same denominator. d) Simplify, if possible. b Add using fraction notation when denominators are different. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 10

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications b Add using fraction notation when denominators are different. 6 a) Since 4 is a factor of 8, the LCM of 4 and 8 is 8. Thus, the LCD is 8. b) We need to find a fraction equivalent to with a denominator of 8: Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 11

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications b Add using fraction notation when denominators are different. 6 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 12

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications b Add using fraction notation when denominators are different. 7 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 13

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications b Add using fraction notation when denominators are different. 9 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 14

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications b Add using fraction notation when denominators are different. 10 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 15

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications b Add using fraction notation when denominators are different. 10 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 16

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications b Add using fraction notation when denominators are different. 10 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 17

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications c Use < or > to form a true statement with fraction notation. When two fractions share a common denominator, the larger number can be found by comparing numerators. For example, 4 is greater than 3, so Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 18

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications c Use < or > to form a true statement with fraction notation. 11 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 19

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications c Use < or > to form a true statement with fraction notation. 11 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 20

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications d Solve problems involving addition with fraction notation. 13 A contractor uses two layers of subflooring under a ceramic tile floor. First, she installs a -in. layer of oriented strand board (OSB). Then a -in. sheet of cement board is mortared to the OSB. The mortar is -in. thick. What is the total thickness of the two installed subfloors? Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 21

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications d Solve problems involving addition with fraction notation. 13 1. Familiarize. We let t = the total thickness of the subfloors. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 22

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications d Solve problems involving addition with fraction notation. 13 2. Translate. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 23

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications d Solve problems involving addition with fraction notation. 13 3. Solve. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 24

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.2 Addition, Order, and Applications d Solve problems involving addition with fraction notation. 13 4. Check. We check by repeating the calculation. 5. State. The total thickness of the installed subfloors is in. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 25