CHAPTER R Prealgebra Review Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. R.1Factoring and LCMs R.2Fraction Notation R.3Decimal Notation R.4Percent Notation R.5Exponential Notation and Order of Operations R.6Geometry

OBJECTIVES R.2 Fraction Notation Slide 3Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. aFind equivalent fraction expressions by multiplying by 1. bSimplify fraction notation. cAdd, subtract, multiply, and divide using fraction notation.

The following are some examples of fractions: This way of writing number names is called fraction notation. The top number is called the numerator and the bottom number is called the denominator.  Numerator  Denominator R.2 Fraction Notation a Find equivalent fraction expressions by multiplying by 1. Slide 4Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

The arithmetic numbers are the whole numbers and the fractions, such as 8, 3/4, and 6/5. All these numbers can be named with fraction notation a/b, where a and b are whole numbers and b ≠ 0. R.2 Fraction Notation Slide 5Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

For any number a, a + 0 = a. Adding 0 to any number gives that same number = 12 R.2 Fraction Notation The Identity Property of Zero (Additive Identity) Slide 6Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

For any number a, a  1 = a. Multiplying any number by 1 gives that same number. 2  1 = 2 R.2 Fraction Notation The Identity Property of 1 (Multiplicative Identity) Slide 7Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

For any number a, a  0, R.2 Fraction Notation Equivalent Expressions for 1 Slide 8Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Solution Since 36 ∙ 4 = 9, we multiply by 1, using : R.2 Fraction Notation a Find equivalent fraction expressions by multiplying by 1. AFind a number equivalent to with a denominator of 36. Slide 9Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Solution 1. Removing a factor equal to 1: 7/7 = 1 R.2 Fraction Notation b Simplify fraction notation. BSimplify. (continued) Slide 10Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Solution Writing 1 allows for pairing of factors in the numerator and the denominator. R.2 Fraction Notation b Simplify fraction notation. BSimplify. Slide 11Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

Canceling is a shortcut that you may have used for removing a factor that equals 1 when working with fraction notation. Canceling may be done only when removing common factors in numerators and denominators. Canceling must be done with care and understanding. R.2 Fraction Notation b Simplify fraction notation. Slide 12Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

Caution! The difficulty with canceling is that it is often applied incorrectly in situations like the following: The correct answers are: In each of the incorrect cancellations, the numbers canceled did not form a factor equal to 1. Factors are parts of products, but in 2 + 3, the numbers 2 and 3 are terms. You cannot cancel terms. Slide 13Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

To multiply fractions, multiply the numerators and multiply the denominators: R.2 Fraction Notation Multiplying Fractions Slide 14Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Removing a factor equal to 1 Solution R.2 Fraction Notation c Add, subtract, multiply, and divide using fraction notation. CMultiply and simplify. Slide 15Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

To add fractions when the denominators are the same, add the numerators and keep the same denominator: R.2 Fraction Notation Adding Fractions with Like Denominators Slide 16Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Solution 1. R.2 Fraction Notation c Add, subtract, multiply, and divide using fraction notation. DAdd and simplify. (continued) Slide 17Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Solution R.2 Fraction Notation c Add, subtract, multiply, and divide using fraction notation. DAdd and simplify. Slide 18Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

To add fractions when denominators are different: a) Find the least common multiple (LCM) of the denominators. That number is the least common denominator, LCD. b) Multiply by 1, using an appropriate notation, n/n, to express each number in terms of the LCD. c) Add the numerators, keeping the same denominator. d) Simplify, if possible. R.2 Fraction Notation Adding Fractions with Different Denominators Slide 19Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Solution a) The LCD is 10. Since 5 is a factor of 10, the LCM of 5 and 10 is 10. R.2 Fraction Notation c Add, subtract, multiply, and divide using fraction notation. E Add: (continued) Slide 20Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Solution b) We need to find a fraction equivalent to with a denominator of 10: c & d) We add: R.2 Fraction Notation c Add, subtract, multiply, and divide using fraction notation. EAdd: Slide 21Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Think: 12  = 36. The answer is 3, so we multiply by 1, using 3/3. Think: 18  = 36. The answer is 2, so we multiply by 1, using 2/2. Solution: The LCD is = 2 ∙ 2 ∙ 3 18 = 2 ∙ 3 ∙ 3 LCM = 2 ∙ 2 ∙ 3 ∙ 3, or 36 R.2 Fraction Notation c Add, subtract, multiply, and divide using fraction notation. FAdd: Slide 22Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Solution: The LCM of 7 and 5 is 35, so the LCD is 35. Find equivalent numbers with denominators of 35. Think: 5  = 35. The answer is 7, so we multiply by 1, using 7/7. Think: 7  = 35. The answer is 5, so we multiply by 1, using 5/5. R.2 Fraction Notation c Add, subtract, multiply, and divide using fraction notation. GSubtract: (continued) Slide 23Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Solution We subtract: R.2 Fraction Notation c Add, subtract, multiply, and divide using fraction notation. GSubtract: Slide 24Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE The LCM is 2  2  2  2  3 = 48 Solution: Determine the LCM of 12 and 16. R.2 Fraction Notation c Add, subtract, multiply, and divide using fraction notation. HSubtract: Slide 25Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

Two numbers whose product is 1 are called reciprocals, or multiplicative inverses, of each other. R.2 Fraction Notation Reciprocals Slide 26Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE R.2 Fraction Notation c Add, subtract, multiply, and divide using fraction notation. IFind the reciprocal. (continued) Slide 27Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Solution 1. The reciprocal of is 2. The reciprocal of is 3. The reciprocal of is 4. The reciprocal of is R.2 Fraction Notation c Add, subtract, multiply, and divide using fraction notation. IFind the reciprocal. Slide 28Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

To divide fractions, multiply by the reciprocal of the divisor: R.2 Fraction Notation Dividing Fractions Slide 29Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Multiply by the reciprocal of the divisor Factoring and identifying a common factor Removing a factor equal to 1 Solution R.2 Fraction Notation c Add, subtract, multiply, and divide using fraction notation. JDivide and simplify. Slide 30Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Multiply by the reciprocal of the divisor Factoring and identifying a common factor Removing a factor equal to 1 Solution R.2 Fraction Notation c Add, subtract, multiply, and divide using fraction notation. KDivide and simplify. Slide 31Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.