CHAPTER 3 Fraction Notation: Multiplication and Division Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 3.1Multiples and Divisibility 3.2Factorizations 3.3Fractions and Fraction Notation 3.4Multiplication and Applications 3.5Simplifying 3.6Multiplying, Simplifying, and More with Area 3.7Reciprocals and Division 3.8Solving Equations: The Multiplication Principle

OBJECTIVES 3.6 Multiplying, Simplifying, and More with Area Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aMultiply and simplify using fraction notation. bSolve applied problems involving multiplication.

3.6 Multiplying, Simplifying, and More with Area a Multiply and simplify using fraction notation. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. It is often possible to simplify after we multiply. To make such simplifying easier, it is usually best not to carry out the products in the numerator and the denominator immediately, but to factor and simplify first.

3.6 Multiplying, Simplifying, and More with Area a Multiply and simplify using fraction notation. Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Title 3.6 Multiplying, Simplifying, and More with Area Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To multiply and simplify: a) Write the products in the numerator and the denominator, but do not carry out the multiplication. b) Factor the numerator and the denominator. c) Factor the fraction to remove a factor equal to 1, if possible. d) Carry out the remaining products.

EXAMPLE 3.6 Multiplying, Simplifying, and More with Area a Multiply and simplify using fraction notation. Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Multiply and simplify.

EXAMPLE 3.6 Multiplying, Simplifying, and More with Area a Multiply and simplify using fraction notation. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

3.6 Multiplying, Simplifying, and More with Area b Solve applied problems involving multiplication. Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Recall that problems involving repeated addition and those with keywords “of,” “twice,” and “product” translate to multiplication.

EXAMPLE 3.6 Multiplying, Simplifying, and More with Area b Solve applied problems involving multiplication. 5Landscaping. Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Celina’s Landscaping uses lb of peat moss when planting a rosebush. How much will be needed to plant 21 rosebushes?

EXAMPLE 3.6 Multiplying, Simplifying, and More with Area b Solve applied problems involving multiplication. 5Landscaping. Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Familiarize. We let n = the number of pounds of peat moss needed.

EXAMPLE 3.6 Multiplying, Simplifying, and More with Area b Solve applied problems involving multiplication. 5Landscaping. Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 2. Translate. 3. Solve.

EXAMPLE 3.6 Multiplying, Simplifying, and More with Area b Solve applied problems involving multiplication. 5Landscaping. Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 5. State. Celina’s Landscaping will need 14 lb of peat moss to plant 21 rosebushes. 4. Check. We check by repeating the calculation. (This is left to the student.)

3.6 Multiplying, Simplifying, and More with Area b Solve applied problems involving multiplication. Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We multiply to find the area of a triangle. Consider a triangle with a base of length b and a height of h. A rectangle can be formed by splitting and inverting a copy of this triangle. The rectangle’s area is exactly twice the area of the triangle.

3.6 Multiplying, Simplifying, and More with Area AREA OF A TRIANGLE Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The area A of a triangle is half the length of the base b times the height h:

EXAMPLE 3.6 Multiplying, Simplifying, and More with Area b Solve applied problems involving multiplication. 6 Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Find the area of the triangle.

EXAMPLE 3.6 Multiplying, Simplifying, and More with Area b Solve applied problems involving multiplication. 7 Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Find the area

EXAMPLE 3.6 Multiplying, Simplifying, and More with Area b Solve applied problems involving multiplication. 8 Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Find the area of the kite.

EXAMPLE 3.6 Multiplying, Simplifying, and More with Area b Solve applied problems involving multiplication. 8 Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Familiarize. We let k = the kite’s area. 2. Translate.

EXAMPLE 3.6 Multiplying, Simplifying, and More with Area b Solve applied problems involving multiplication. 8 Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 3. Solve. 4. Check. We can check by repeating the calculations. The unit, in 2, is appropriate for area. 5. State. The area of the kite is 216 in 2.