Chapter 1 Section 1

Copyright © 2012, 2008, 2004 Pearson Education, Inc Fractions Objectives Learn the definition of factor. Write fractions in lowest terms. Multiply and divide fractions. Add and subtract fractions. Solve applied problems that involve fractions. Interpret data in a circle graph

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Natural numbers: 1, 2, 3, 4,…,, Numerator Fraction Bar Denominator Example: The improper fraction can be written, a mixed number. Whole numbers: 0, 1, 2, 3, 4,…, Fractions: Proper fraction: Numerator is less than denominator and the value is less than 1. Improper fraction: Numerator is greater than or equal to denominator and the value is greater than or equal to 1. Mixed number: A combination of a whole number and a proper fraction. Slide Definitions

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 1 Learn the definition of factor. Slide 1.1-4

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Learn the definition of factor. In the statement 3 × 6 = 18, the numbers 3 and 6 are called factors of 18. Other factors of 18 include 1, 2, 9, and 18. The number 18 in this statement is called the product. The number 18 is factored by writing it as a product of two or more numbers. Examples: 6 · 3, 18 × 1, (2)(9),2(3)(3) Slide A raised dot is often used instead of the × symbol to indicate multiplication because × may be confused with the letter x.

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Learn the definition of factor. (cont’d) A natural number greater than 1 is prime if its products include only 1 and itself. Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37… A natural number greater than 1 that is not prime is called a composite number. Examples: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21… Slide 1.1-6

Copyright © 2012, 2008, 2004 Pearson Education, Inc. EXAMPLE 1 Write 90 as the product of prime factors. Starting with the least prime factor is not necessary. No matter which prime factor we start with, the same prime factorization will always be obtained. Solution: Factoring Numbers Slide 1.1-7

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 2 Write fractions in lowest terms. Slide 1.1-8

Copyright © 2012, 2008, 2004 Pearson Education, Inc. A fraction is in lowest terms when the numerator and denominator have no common factors other than 1. Write fractions in lowest terms. Slide Basic Principle of Fractions If the numerator and denominator of a fraction are multiplied or divided by the same nonzero number, the value of the fraction remains unchanged.

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Writing a Fraction in Lowest Terms Step 1:Write the numerator and the denominator as the product of prime factors. Write fractions in lowest terms. (cont’d) Step 2: Divide the numerator and the denominator by the greatest common factor, the product of all factors common to both. Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. EXAMPLE 2 Write in lowest terms. When writing fractions in lowest terms, be sure to include the factor 1 in the numerator or an error may result. Solution: = Writing Fractions in Lowest Terms Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 3 Multiply and divide fractions. Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Multiply and divide fractions. Multiplying Fractions If and are fractions, then · =. That is, to multiply two fractions, multiply their numerators and then multiply their denominators. Slide Some prefer to factor and divide out any common factors before multiplying.

Copyright © 2012, 2008, 2004 Pearson Education, Inc. EXAMPLE 3 Find each product, and write it in lowest terms. Solution: or Multiplying Fractions Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Dividing Fractions If and are fractions, then ÷ =. Multiply and divide fractions. (cont’d) That is, to divide by a fraction, multiply by its reciprocal; the fraction flipped upside down. Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. EXAMPLE 4 Find each quotient, and write it in lowest terms. Solution: or Dividing Fractions Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 4 Add and subtract fractions. Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Add and subtract fractions. Adding Fractions If and are fractions, then + =. To find the sum of two fractions having the same denominator, add the numerators and keep the same denominator. Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. EXAMPLE 5 Find the sum, and write it in lowest terms. Solution: Adding Fractions with the Same Denominator Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Add and subtract fractions. (cont’d) Finding the Least Common Denominator If the fractions do not share a common denominator, the least common denominator (LCD) must first be found as follows: Step 1: Factor each denominator. Step 2: Use every factor that appears in any factored form. If a factor is repeated, use the largest number of repeats in the LCD. Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. EXAMPLE 6 Find each sum, and write it in lowest terms. or Adding Fractions with Different Denominators Solution: Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Add and subtract fractions. (cont’d) Subtracting Fractions If and are fractions, then. If fractions have different denominators, find the LCD using the same method as with adding fractions. To find the difference between two fractions having the same denominator, subtract the numerators and keep the same denominator. Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Subtracting Fractions Find each difference, and write it in lowest terms. EXAMPLE 7 or Solution: Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 5 Solve applied problems that involve fractions. Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. EXAMPLE 8 A gallon of paint covers 500 ft 2. To paint his house, Tran needs enough paint to cover 4200 ft 2. How many gallons of paint should he buy? Tran needs to buy 9 gallons of paint. Solution: Adding Fractions to Solve an Applied Problem Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 6 Interpret data in a circle graph. Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. EXAMPLE 9 Recently there were about 970 million Internet users world wide. The circle graph below shows the fractions of these users living in various regions of the world. Using a Circle Graph to Interpret Information How many actual Internet users were there in Europe? Estimate the number of Internet users in Europe. Which region had the second-largest number of Internet Users? Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: a) Europe EXAMPLE 9 b) c) Slide Using a Circle Graph to Interpret Information (cont’d)