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

4.7 Multiplication and Division of Mixed Numerals; Applications

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

a Multiply using mixed numerals.b Divide using mixed numerals.c Evaluate expressions using mixed numerals.d Solve applied problems involving multiplication

and division with mixed numerals.

4.7 Multiplication and Division of Mixed Numerals; Applications

a Multiply using mixed numerals.

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

Carrying out addition and subtraction with mixed numerals is usually easier if the numbers are left as mixed numerals. With multiplication and division, however, it is easier to convert the numbers to fraction notation first. If the result is a fraction with the numerator greater than the denominator, the answer should be written as a mixed numeral.

Title

4.7 Multiplication and Division of Mixed Numerals; Applications

Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

To multiply using mixed numerals, first convert to fraction notation and multiply. Then convert the answer to a mixed numeral, if appropriate.

EXAMPLE

4.7 Multiplication and Division of Mixed Numerals; Applications

a Multiply using mixed numerals.

1

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EXAMPLE

4.7 Multiplication and Division of Mixed Numerals; Applications

a Multiply using mixed numerals.

3

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EXAMPLE

4.7 Multiplication and Division of Mixed Numerals; Applications

a Multiply using mixed numerals.

4

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4.7 Multiplication and Division of Mixed Numerals; Applications

a Multiply using mixed numerals.

Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

4.7 Multiplication and Division of Mixed Numerals; Applications

b Divide using mixed numerals.

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Title

4.7 Multiplication and Division of Mixed Numerals; Applications

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

To divide using mixed numerals, first write fraction notation and divide. Then convert the answer to a mixed numeral, if appropriate.

EXAMPLE

4.7 Multiplication and Division of Mixed Numerals; Applications

b Divide using mixed numerals.

6

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EXAMPLE

4.7 Multiplication and Division of Mixed Numerals; Applications

b Divide using mixed numerals.

7

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EXAMPLE

4.7 Multiplication and Division of Mixed Numerals; Applications

c Evaluate expressions using mixed numerals.

9

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We substitute and follow the rules for order of operations:

EXAMPLE

4.7 Multiplication and Division of Mixed Numerals; Applications

c Evaluate expressions using mixed numerals.

9

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

EXAMPLE

4.7 Multiplication and Division of Mixed Numerals; Applications

d Solve applied problems involving multiplicationand division with mixed numerals.

11 Koi Pond.

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

Colleen designed a koi fish pond for her backyard. Using the dimensions shown in the diagram, determine the area of Colleen’s backyard before the pond was constructed and the area of the yard remaining after the pond was completed.Sources: en.wikipedia.org; pondliner.com

EXAMPLE

4.7 Multiplication and Division of Mixed Numerals; Applications

d Solve applied problems involving multiplicationand division with mixed numerals.

11 Koi Pond.

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

EXAMPLE

4.7 Multiplication and Division of Mixed Numerals; Applications

d Solve applied problems involving multiplicationand division with mixed numerals.

11 Koi Pond.

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

1. Familiarize. We let B = the area of the yard before the construction, P = the area of the pond, and R = the area of the yard that remains after the pond is complete.

EXAMPLE

4.7 Multiplication and Division of Mixed Numerals; Applications

d Solve applied problems involving multiplicationand division with mixed numerals.

11 Koi Pond.

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

2. Translate. This is a multistep problem. To find R, the area of the yard remaining, we first find B, the area of the yard before construction, and P, the area of the pond. Then R is the area of the yard B minus the area of thepond P:

We find each area using the formula for the area of a rectangle,

EXAMPLE

4.7 Multiplication and Division of Mixed Numerals; Applications

d Solve applied problems involving multiplicationand division with mixed numerals.

11 Koi Pond.

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

3. Solve.

EXAMPLE

4.7 Multiplication and Division of Mixed Numerals; Applications

d Solve applied problems involving multiplicationand division with mixed numerals.

11 Koi Pond.

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

EXAMPLE

4.7 Multiplication and Division of Mixed Numerals; Applications

d Solve applied problems involving multiplicationand division with mixed numerals.

11 Koi Pond.

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

4. Check. We can perform a check by repeating the calculations or we can round the measurements to the nearest yard and estimate a solution.

EXAMPLE

4.7 Multiplication and Division of Mixed Numerals; Applications

d Solve applied problems involving multiplicationand division with mixed numerals.

11 Koi Pond.

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

5. State. The area of the yard before construction of the pond was sq yd. The area of the yard remaining after the pond was completed was