2Warm Up Multiply. 1. 2. 3. 4. 7 18 27 7 or 1 20 2 77 or 15 5 25 1 or 3
3NS2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.Also covered: NS2.2, NS2.4CaliforniaStandards
5Reciprocals can help you divide by fractions Reciprocals can help you divide by fractions. Two numbers are reciprocals or multiplicativeinverses if their product is 1. The reciprocal of is 3 because1313 3=1.Dividing by a number is the same as multiplying by its reciprocal.reciprocals136 = 26 ÷ 3 = 2same answer
7Additional Example 1: Dividing Fractions Divide. Write each answer in simplest form.3725÷A.3725375225÷=Multiply by the reciprocal of .375=21151414=or 138B.÷123811238Multiply by the reciprocal of 12.÷12=1381Simplify.=1241=32
8÷ A. B. ÷ ÷ Check It Out! Example 1 Divide. Write each answer in simplest form.3512÷A.3512352112÷=Multiply by the reciprocal of .352=1165=or 1345B.÷3343413Multiply by the reciprocal of 3.÷3=1341Simplify.=311=4
9Additional Example 2: Dividing Mixed Numbers Divide. Write each answer in simplest form.2314Important:Write mixed numbers as improper fractions.A.5÷12314173545÷1=÷54=17345Multiply by the reciprocal of.6815815=or 43412B.÷234123452Write 2 as an improper fraction.12÷2=÷523425=Multiply by the reciprocal of .132Simplify.=452310=
10Check It Out! Example 2 Write mixed numbers as improper fractions. ÷ ÷ Divide. Write each answer in simplest form.2312A.3÷1Write mixed numbers as improper fractions.2312113323÷1=÷11332=23Multiply by the reciprocal of.22949or 2=3525B.÷135253575Write 1 as an improper fraction.25÷1=÷753557=Multiply by the reciprocal of .135Simplify.=57137=
11Additional Example 3: Social Studies Application The life span of a golden dollar coin is 30 years, whilepaper currency lasts an average of 1 years. How many12times longer will the golden dollar stay in circulation?123013230 ÷ 1=÷Write the number as an improper fraction.3012332=Multiply by the reciprocal of .10302=Simplify.131201=or 20The golden dollar will stay in circulation about20 times longer than paper currency.
12The queen ant will live 7 times longer than the worker ant. Check It Out! Example 3The average life of a queen ant is approximately 3 years.The life span of a worker ant is year. How many37times longer will the queen ant live?3731373 ÷=÷Write the number as an improper fraction.317337=Multiply by the reciprocal of .137=Simplify.13171=or 7The queen ant will live 7 times longer than theworker ant.
13Divide. Write each answer in simplest form. Lesson QuizDivide. Write each answer in simplest form.451.8 ÷10594940or2.18÷1103.35÷634.21÷7354414345. There are 5yards of silk in a roll. If it takesof a yard to make one designer scarf, how manyscarves can be made from the roll?7