Evaluating Algebraic Expressions 2-5Dividing Rational Numbers NS1.2 D ivide rational numbers (integers, fractions, and terminating decimals) AF1.3 Simplify numerical expressions by applying properties of rational numbers (inverse) California Standards

Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Two numbers whose product is 1 are multiplicative inverses, or reciprocals. Notes

Evaluating Algebraic Expressions 2-5Dividing Rational Numbers A division problem can always be rewritten as a multiplication problem by using the reciprocal of the divisor. notes

Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Additional Example 1A: Dividing Fractions Divide. Write the answer in simplest form. Multiply by the reciprocal ÷ = No common factors ÷ = Simplest form = Notes

Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Additional Example 1B: Dividing Fractions Divide. Write the answer in simplest form ÷ ÷ 22 = ÷ Write as an improper fraction. Multiply by the reciprocal. No common factors = = 3 16 = = Notes

Evaluating Algebraic Expressions 2-5Dividing Rational Numbers 7 15 ÷ = 7 15 ÷ = Check It Out! Example1A Divide. Write the answer in simplest form. Multiply by the reciprocal. No common factors Simplest form = Rally Coach A

Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Write as an improper fraction ÷ Multiply by the reciprocal = No common factors 2525 ÷ 3 4 = ÷ Divide. Write the answer in simplest form. = = or Check It Out! Example1B Rally Coach B

Evaluating Algebraic Expressions 2-5Dividing Rational Numbers When dividing a decimal by a decimal, multiply both numbers by a power of 10 so you can divide by a whole number = = decimal place1 zero 10 Notes

Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Find ÷ Estimate the reasonableness of your answer. Additional Example 2: Dividing Decimals 0.24 has two decimal places so multiple both numbers by 100 to make the divisor an integer ) ) 38.4 Then divide as a whole number. 1  ÷ 0.24 = 1.6 Estimate: 40 ÷ 20 = 2 The answer is reasonable. – Notes

Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Find 0.65 ÷ Estimate the reasonableness of your answer. Check It Out! Example has two decimal places so multiple both numbers by 100 to make the divisor an integer ) ) 65.0 Then divide as a whole number. 2  ÷ 0.25 = 2.6 Estimate: 60 ÷ 20 = 3 The answer is reasonable. –150 n 0 Elbow Partners

Evaluating Algebraic Expressions 2-5Dividing Rational Numbers 5.25 for n = 0.15 n Substitute 0.15 for n. Additional Example 3: Evaluating Expressions with Rational Numbers Evaluate the expression for the given value of the variable n 0.15 = When n = 0.15, = n 0.15 ) has two decimal places, so multiply both numbers by 100 to make the divisor an integer.  ) Notes

Evaluating Algebraic Expressions 2-5Dividing Rational Numbers 3.60 for n = 0.12 n Substitute 0.12 for n. Check It Out! Example 3 Evaluate the expression for the given value of the variable n 0.12 = When n = 0.12, = n 0.12 ) has two decimal places, so multiply both numbers by 100 to make the divisor an integer.  ) Face Partners

Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Example 4 A ship will use of its total fuel load for a typical round trip. If there is of a total fuel load on board now, how many complete trips can be made? Numbers Understand the Problem Make a PlanSolveLook Back Notes