Section Objectives 2.2 Simplifying Fractions Slide 1 1.Factorizations and Divisibility 2.Prime Factorization Equivalent Fractions Find the Greatest Common Factor (GCF) 5.Simplifying Fractions to Lowest Terms 6.Applications of Simplifying Fractions

Section 2.2 Simplifying Fractions 1.Factorizations and Divisibility Slide 2 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. A factor of a number n is a nonzero whole number that divides evenly into n. A factorization of a number n is a product of factors that equals n.

Example 1Finding Factorizations of a Number Slide 3 Find four different factorizations of 12. Find four different factorizations of 18

Example Find four different factorizations of 24. 2You Try Slide 4

PROCEDUREDivisibility Rules for 2, 3, 5, and 10 Slide 5 Divisibility by 2. A whole number is divisible by 2 if it is an even number. That is, the ones-place digit is 0, 2, 4, 6, or 8. Examples: 26 and 384 Divisibility by 3. A whole number is divisible by 3 if the sum of its digits is divisible by 3. Example: 312 (sum of digits is = 6, which is divisible by 3)

PROCEDUREDivisibility Rules for 2, 3, 5, and 10 Slide 6 Divisibility by 5. A whole number is divisible by 5 if its ones-place digit is 5 or 0. Examples: 45 and 260 Divisibility by 10. A whole number is divisible by 10 if its ones-place digit is 0. Examples: 30 and 170

Example 3Applying the Divisibility Rules Slide 7 c. 240 d. 570

Example Determine whether the given number is divisible by 2, 3, 5, or 10. 4You Try Slide 8

Section 2.2 Simplifying Fractions 2. Prime Factorization Two important classifications of whole numbers are prime numbers and composite numbers. Slide 9

DEFINITIONPrime and Composite Numbers Slide 10 A prime number is a whole number greater than 1 that has only two factors (itself and 1). A composite number is a whole number greater than 1 that is not prime. That is, a composite number will have at least one factor other than 1 and the number itself. Note: The whole numbers 0 and 1 are neither prime nor composite.

Example 5Identifying Prime and Composite Numbers Slide 11 Determine whether the number is prime, composite, or neither. d. 17e. 29 f. 153

Example Determine whether the number is prime, composite, or neither. 6You Try Slide 12

DEFINITIONPrime Factorization Slide 13 The prime factorization of a number is the factorization in which every factor is a prime number. Note: The order in which the factors are written does not affect the product.

Example 7Determining the Prime Factorization of a Number Slide 14 Find the prime factorization of 220.

Example 4. Find the prime factorization of 96 8You Try Slide 15

Section 2.2 Simplifying Fractions 2.Prime Factorization Slide 16 Another technique to find the prime factorization of a number is to divide the number by the smallest known prime factor of the number. Then divide the quotient by its smallest prime factor. Continue dividing in this fashion until the quotient is a prime number. The prime factorization is the product of divisors and the final quotient.

Example Determining Prime Factorizations Slide 17 9

Example Find the prime factorization of the given number. 10You Try Slide 18

Section 2.2 Simplifying Fractions 3.Equivalent Fractions Slide 19 Fractions are equivalent if they all represent the same portion of a whole.

Example One method to show that two fractions are equivalent is to calculate their cross products. For example, to show that, we have Determining whether two fractions are equivalent. 11 Equivalent Fractions Slide 20

Example 12Determining Whether Two Fractions Are Equivalent Slide 21

Example 1.2. Fill in the blank with or. 13You Try Slide 22

Section The greatest common factor (GCF) of two or more numbers is the largest number that will divide each of the given numbers evenly. A common factor is a number that divide two or more numbers evenly. 2.2 Simplifying Fractions 4.Find the Greatest Common Factor of two or more numbers. Slide 23

PROCEDURE 1.Write the prime factorization for each of the numbers in the group. 2.Locate the prime factors that are common to all the numbers. 3.The greatest common factor will be the product of all the common prime factors. Finding the greatest common factor (GCF) of two are more numbers Slide 24

Example 28 and 2435 and 26 14Find the GCF Slide 25

Example 15, 45, and 90 15Find the GCF Slide 26

Example 12 and and 54 16You Try Slide 27 Find the GCF.

Example Find the GCF. 36, 72, and You Try Slide 28

Section 2.2 Simplifying Fractions 5.Simplifying Fractions to Lowest Terms Slide 29 A fraction is said to be in lowest terms if the numerator and denominator share no common factors other than 1. To simplify a fraction, we begin by factoring the numerator and denominator into prime factors. This will help identify the common factors. For example;

PROPERTYFundamental Principle of Fractions Slide 30 Suppose that a number, c, is a common factor in the numerator and denominator of a fraction. Then

Example 18Simplifying a Fraction to Lowest Terms Slide 31

Example 19Simplifying Fractions to Lowest Terms Slide 32 Simplify the fraction. Write the answer as a fraction or whole number.

Example 20Simplifying Fractions by 10, 100, and 1000 Slide 33 Simplify each fraction to lowest terms by first reducing by 10, 100, or Write the answer as a fraction.

Example Simplify to lowest terms. Write the answer as a fraction or whole number. Simplify to lowest terms. 21You Try Slide

Example Simplify to lowest terms by first reducing by 10, 100, or You Try Slide 35

Example 23Simplifying Fractions in an Application Slide 36 Madeleine got 28 out of 35 problems correct on an algebra exam. David got 27 out of 45 questions correct on a different algebra exam. What fractional part of the exam did each student answer correctly? 6. Applications of Simplifying Fractions

Example Joanne planted 77 seeds in her garden and 55 sprouted. Geoff planted 140 seeds and 80 sprouted. What fractional part of the seeds sprouted for Joanne and what fractional part sprouted for Geoff? 24You Try Slide 37

1.Factorizations and Divisibility 2.Prime Factorization Equivalent Fractions Find the Greatest Common Factor (GCF) 5.Simplifying Fractions to Lowest Terms 6.Applications of Simplifying Fractions A review of the objectives you are responsible for learning. Slide 38