CHAPTER 4 Fraction Notation: Addition, Subtraction, and Mixed Numerals Slide 2Copyright 2012, 2008,...

CHAPTER

4Fraction Notation: Addition, Subtraction, and Mixed Numerals

Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

4.1 Least Common Multiples4.2 Addition, Order, and Applications4.3 Subtraction, Equations, and Applications4.4 Solving Equations: Using the Principles Together4.5 Mixed Numerals4.6 Addition and Subtraction of Mixed Numerals;

Applications4.7 Multiplication and Division of Mixed Numerals;

Applications4.8 Order of Operations and Complex Fractions

OBJECTIVES

4.2 Addition, Order, and Applications

Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

a Add using fraction notation when denominators arethe same.

b Add using fraction notation when denominators aredifferent.

c Use < or > to form a true statement with fraction notation.

d Solve problems involving addition with fractionnotation.

4.2 Addition, Order, and Applications

a Add using fraction notation when denominators arethe same.

Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Addition using fraction notation corresponds to combining or putting like things together, just as when we combined like terms.

Title

4.2 Addition, Order, and Applications

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To add when denominators are the same,a) add the numerators,b) keep the denominator,andc) simplify, if possible.

EXAMPLE

4.2 Addition, Order, and Applications

a Add using fraction notation when denominators arethe same.

Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Add and, if possible, simplify.

4.2 Addition, Order, and Applications

a Add using fraction notation when denominators arethe same.

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We may need to add fractions when combining like terms.

EXAMPLE

4.2 Addition, Order, and Applications

a Add using fraction notation when denominators arethe same.

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4.2 Addition, Order, and Applications

b Add using fraction notation when denominators aredifferent.

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Title

4.2 Addition, Order, and Applications

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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.

EXAMPLE

4.2 Addition, Order, and Applications

b Add using fraction notation when denominators aredifferent.

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Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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:

EXAMPLE

4.2 Addition, Order, and Applications

b Add using fraction notation when denominators aredifferent.

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Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE

4.2 Addition, Order, and Applications

b Add using fraction notation when denominators aredifferent.

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Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE

4.2 Addition, Order, and Applications

b Add using fraction notation when denominators aredifferent.

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Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE

4.2 Addition, Order, and Applications

b Add using fraction notation when denominators aredifferent.

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Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE

4.2 Addition, Order, and Applications

b Add using fraction notation when denominators aredifferent.

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Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE

4.2 Addition, Order, and Applications

b Add using fraction notation when denominators aredifferent.

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Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

4.2 Addition, Order, and Applications

c Use < or > to form a true statement with fraction notation.

Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

When two fractions share a common denominator, the larger number can be found by comparing numerators.

For example, 4 is greater than 3, so

EXAMPLE

4.2 Addition, Order, and Applications

c Use < or > to form a true statement with fraction notation.

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Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE

4.2 Addition, Order, and Applications

c Use < or > to form a true statement with fraction notation.

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Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE

4.2 Addition, Order, and Applications

d Solve problems involving addition with fractionnotation.

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Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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?

EXAMPLE

4.2 Addition, Order, and Applications

d Solve problems involving addition with fractionnotation.

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Slide 22Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

1. Familiarize. We let t = the total thickness of the subfloors.

EXAMPLE

4.2 Addition, Order, and Applications

d Solve problems involving addition with fractionnotation.

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Slide 23Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

2. Translate.

EXAMPLE

4.2 Addition, Order, and Applications

d Solve problems involving addition with fractionnotation.

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Slide 24Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

3. Solve.

EXAMPLE

4.2 Addition, Order, and Applications

d Solve problems involving addition with fractionnotation.

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Slide 25Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

4. Check. We check by repeating the calculation.5. State. The total thickness of the installed subfloors is in.