3 Warm UpName a common factor for each pair.1. 5 and and 123. 20 and and 145. 6 and and 15Possible answers:534221
4 CaliforniaStandardsNumber Sense (NS2.4) - 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: Number Sense (NS1.1)
5 Vocabularyequivalent fractionsimproper fractionmixed number
6 Different fractions can name the same number. 356101525==
7 In the diagram = . These are called equivalent fractions because they are different expressions for the same nonzero number.=To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same nonzero number.
8 Find two fractions equivalent to . Additional Example 1: Finding Equivalent Fractions57Find two fractions equivalent to .5 21014=Multiply the numerator and denominator by 2.7 25 31521=Multiply the numerator and denominator by 3.7 3Remember!A fraction with the same numerator anddenominator, such as is equal to 1.2 2
9 5710141521The 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 1.5 7
10 Find two fractions equivalent to . Check It Out! Example 1612Find two fractions equivalent to .6 21224=Multiply the numerator and denominator by 2.12 26 ÷ 212 ÷ 236=Divide the numerator and denominator by 2.
11 Additional Example 2: Writing Fractions in Simplest Form 1824Write the fraction in simplest form.Find the GCD of 18 and 24.18 = 2 • 3 • 3The GCD is 6 = 2 • 3.24 = 2 • 2 • 2 • 3182418 ÷ 624 ÷ 634==Divide the numerator and denominator by 6.
12 Write the fraction in simplest form. Check It Out! Example 21545Write 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 ÷ 1513==Divide the numerator and denominator by 15.
13 To determine if two fractions are equivalent, simplify the fractions.
14 Additional Example 3A: Determining Whether Fractions are Equivalent Determine whether the fractions in each pair are equivalent.462842andSimplify both fractions and compare.464 ÷ 26 ÷ 223==284228 ÷ 1442 ÷ 1423==46284223andare equivalent because both are equal to .
15 Additional Example 3B: Determining Whether Fractions are Equivalent Determine whether the fractions in each pair are equivalent.6102025andSimplify both fractions and compare.6106 ÷ 210 ÷ 235==202520 ÷ 525 ÷ 545==are not equivalent because their simplestand2025610forms are not equal.
16 Check It Out! Example 3ADetermine whether the fractions in each pair are equivalent.and39618Simplify both fractions and compare.393 ÷ 39 ÷ 313==6186 ÷ 618 ÷ 613==3961813andare equivalent because both are equal to .
17 Check It Out! Example 3BDetermine whether the fractions in each pair are equivalent.412948andSimplify both fractions and compare.4124 ÷ 412 ÷ 413==9489 ÷ 348 ÷ 3316==are not equivalent because their simplestand948412forms are not equal.
18 8 3 = 1 5 5 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
19 (A) Write as a mixed number. Additional Example 4: Converting Between Improper Fractions and Mixed Numbers(A) Write135as a mixed number.First divide the numerator by the denominator.13535Use the quotient and remainder to write the mixed number.= 223(B) Write 7as an improper fraction.First multiply the denominator and whole number,and then add the numerator.+233 7 + 2233=Use the result to write the improper fraction.=73
20 8 Check It Out! Example 4 (A) Write as a mixed number. 156(A) Writeas a mixed number.First divide the numerator by the denominator.15636= 212= 2Use the quotient and remainder to write the mixed number.13(B) Write 8as an improper fraction.First multiply the denominator and whole number,and then add the numerator.+133 8 + 1Use the result towrite the improperfraction.2538==3
21 1. Write two fractions equivalent to . Lesson Quiz1236,12241. Write two fractions equivalent to2. 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