CHAPTER

4Fraction Notation: Addition, Subtraction, and Mixed Numerals

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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.

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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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EXAMPLE

4.2 Addition, Order, and Applications

b Add using fraction notation when denominators aredifferent.

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EXAMPLE

4.2 Addition, Order, and Applications

b Add using fraction notation when denominators aredifferent.

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