2 Warm UpName a common factor for each pair.1. 5 and and 123. 20 and and 145. 6 and and 15Possible answers:534221
3 CaliforniaStandardsNS2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g. to find a common denominator to add two fractions or to find the reduced form of a fraction).Also covered: NS1.1
4 Vocabularyequivalent fractionsimproper fractionmixed number
5 Different fractions can name the same number. 356101525==
6 In the diagram = . These are called equivalent fractions because they are different expressions for the same nonzero number.356101525=To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same nonzero number.
7 8 5 3 5 = 1 8 5 3 5 is an improper 1 is a mixed fraction. Its numerator isgreater than itsdenominator.8535number. Itcontains both awhole numberand a fraction.= 1
8 To determine if two fractions are equivalent, simplify the fractions.
9 Additional Example 1: Finding Equivalent Fractions 57Find two fractions equivalent to .5 211014=Multiply the numerator anddenominator by 2.7 25 311521Multiply the numerator anddenominator by 3.=7 3Remember!A fraction with the same numerator anddenominator, such as is equal to 1.2 2
10 5 7The fractions , , and are equivalent,but only is in simplest form. A fraction is insimplest form when the greatest common divisorof its numerator and denominator is 1.5710141521
11 Additional Example 3A: Determining Whether Fractions are Equivalent Determine whether the fractions in each pair are equivalent.462842andSimplify both fractions and compare.464 ÷ 26 ÷ 2123==284228 ÷ 1442 ÷ 1423=1=are equivalent because both are equal to .and46284223
12 Additional Example 3B: Determining Whether Fractions are Equivalent Determine whether the fractions in each pair are equivalent.6102025andSimplify both fractions and compare.6106 ÷ 210 ÷ 2135==202520 ÷ 525 ÷ 5451==are not equivalent because their simplestand2025610forms are not equal.
13 A. Write as a mixed number. Additional Example 4: Converting Between Improper Fractions and Mixed NumbersA. Write135as a mixed number.First divide the numerator by the denominator.13535Use the quotient and remainder towrite the mixed number.= 223B. Write 7as an improper fraction.First multiply the denominator and whole number,and then add the numerator.+Use the result towrite the improperfraction.233 7 + 2233==73
14 1 1 Check It Out! Example 1 6 12 Find two fractions equivalent to . 6 211224=Multiply the numerator anddenominator by 2.12 26 ÷ 212 ÷ 236Divide the numerator anddenominator by 2.1=
15 1 Check It Out! Example 2 15 45 Write the fraction in simplest form. Find the GCD of 15 and 45.15 = 3 • 5The GCD is 15 = 3 • 5.45 = 3 • 3 • 5154515 ÷ 1545 ÷ 15131Divide the numerator anddenominator by 15.==
16 Check It Out! Example 3ADetermine whether the fractions in each pair are equivalent.and39618Simplify both fractions and compare.393 ÷ 39 ÷ 3131==6186 ÷ 618 ÷ 6131==are equivalent because both are equal to .and396181
17 8 Check It Out! Example 4 A. Write as a mixed number. 156A. Writeas a mixed number.First divide the numerator by the denominator.1563612= 2Use the quotient and remainder to write the mixed number.= 213B. Write 8as an improper fraction.First multiply the denominator and whole number,and then add the numerator.+Use the result towrite the improperfraction.133 8 + 12538==3
18 1. Write two fractions equivalent to . Lesson Quiz12241236,1. Write two fractions equivalent to .2. Determine if and are equivalent.3. Write the fraction in simplest form.4. Write as a mixed number.5. Write 4 as an improper fraction.5 124 10no16481317818237317