Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 2.3 Simplest Form of a Fraction

Martin-Gay, Basic Mathematics, 4e 22 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Writing Fractions in Simplest Form Fractions that represent the same portion of a whole are called equivalent fractions. There are many equivalent forms of a fraction. A special form of a fraction is called simplest form. Simplest Form of a Fraction A fraction is written in simplest form or lowest terms when the numerator and denominator have no common factors other than 1. p 129

Martin-Gay, Basic Mathematics, 4e 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Writing Fractions in Simplest Form DefinitionExample Equivalent Fractions: Fractions that represent the same portion of a whole. Simplest Form or Lowest Terms: When the numerator and the denominator of a fraction have no common factors other than 1. Both have a common factor of 2. There are no more common factors. The simplest form of is P 129 Alternative method

Martin-Gay, Basic Mathematics, 4e 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Examples Write in simplest form. a. b. c. p 129

Martin-Gay, Basic Mathematics, 4e 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Simplest Form Writing a Fraction in Simplest Form To write a fraction in simplest form, write the prime factorization of the numerator and the denominator and then divide both by all common factors. p 129

Martin-Gay, Basic Mathematics, 4e 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Examples Write in simplest form. a. b. c. p 130

Martin-Gay, Basic Mathematics, 4e 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Writing Fractions in Simplest Form Practice Problems Write in simplest form P 130 No common Factors

Martin-Gay, Basic Mathematics, 4e 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Writing Fractions in Simplest Form Practice Problems Write in simplest form P 131

Martin-Gay, Basic Mathematics, 4e 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Determine whether are equivalent. Simplify each fraction. Since both of the simplified fractions are the same, they are equivalent. p 133

Martin-Gay, Basic Mathematics, 4e 10 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Determining Whether Two Fractions Are EquivalentEXAMPLE Determine whether are equivalent. SOLUTION Since both have a common simplified form of they are equivalent. P 132

Martin-Gay, Basic Mathematics, 4e 11 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Equality of Fractions p 133

Martin-Gay, Basic Mathematics, 4e 12 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Determining Whether Two Fractions Are EquivalentEXAMPLE Determine whether are equivalent by cross multiplying. SOLUTION Since the cross products are not equal, are not equivalent. P 133

Martin-Gay, Basic Mathematics, 4e 13 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Determining Whether Two Fractions Are Equivalent Practice Problem 8 Determine whether are equivalent. SOLUTION Since both have a common simplified form of they are equivalent. P 132

Martin-Gay, Basic Mathematics, 4e 14 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Determining Whether Two Fractions Are Equivalent Do Practice Problem 8 Again Determine whether are equivalent by cross multiplying. SOLUTION Since the cross products is equal, are equivalent. P 132

Martin-Gay, Basic Mathematics, 4e 15 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Determining Whether Two Fractions Are Equivalent Practice Problem 9 Determine whether are equivalent. SOLUTION Since they do not have a common simplified form they are not equivalent. P 133

Martin-Gay, Basic Mathematics, 4e 16 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Determining Whether Two Fractions Are Equivalent Do Practice Problem 9 Again Determine whether are equivalent by cross multiplying. SOLUTION Since the cross products are not equal, they are not equivalent. P 133

Martin-Gay, Basic Mathematics, 4e 17 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Solving Problems by Writing Fractions in Simplest FormEXAMPLE SOLUTION There are 5280 feet in a mile. What fraction of a mile is represented by Both 2640 and 5280 have a common factor of The fraction of a mile represented by 2640 is P 133

Martin-Gay, Basic Mathematics, 4e 18 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Solving Problems by Writing Fractions in Simplest Form Practice Problem 10 (alternate) SOLUTION Eighty pigs were used in a recent study of olestra, a calorie-free fat substitute. A group of 12 of these pigs were fed a diet high in fat. What fraction of the pigs were fed the high-fat diet in this study? Write your answer in simplest form. Both 12 and 80 have a common factor of 4. The fraction for the group of 12 pigs is represented by P 133

Martin-Gay, Basic Mathematics, 4e 19 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. DONE

Martin-Gay, Basic Mathematics, 4e 20 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Determine whether are equivalent by cross multiplying. Since 22 ≠20, then p 133