Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 2 Multiplying and Dividing Fractions

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

Martin-Gay, Developmental Mathematics, 2e 33 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.

Martin-Gay, Developmental Mathematics, 2e 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Examples Write in simplest form. a. b. c.

Martin-Gay, Developmental Mathematics, 2e 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.

Martin-Gay, Developmental Mathematics, 2e 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Examples Write in simplest form. a. b. c.

Martin-Gay, Developmental Mathematics, 2e 77 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.

Martin-Gay, Developmental Mathematics, 2e 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Equality of Fractions

Martin-Gay, Developmental Mathematics, 2e 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Determine whether are equivalent by cross multiplying. Since 22 ≠20, then