1. 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

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

3. 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

4. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Additional Example 1A: Dividing Fractions Divide. Write the answer in simplest form. Multiply by the reciprocal. 5 11 ÷ 1212 2121 = No common factors. 5 11 ÷ 1212 10 11 = Simplest form 5 11 2121 = Notes

5. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Additional Example 1B: Dividing Fractions Divide. Write the answer in simplest form. 3838 ÷ 22 3838 ÷ 22 = 19 8 2121 ÷ Write as an improper fraction. Multiply by the reciprocal. No common factors = 19 8 1212 19 1 8 2 = 3 16 = 1 19 16 = Notes

6. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers 7 15 ÷ 3434 4343 = 7 15 ÷ 3434 28 45 = Check It Out! Example1A Divide. Write the answer in simplest form. Multiply by the reciprocal. No common factors Simplest form 7 4 15 3 = Rally Coach A

7. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Write as an improper fraction. 2525 ÷ Multiply by the reciprocal. 34 22 1 5 3 = No common factors 2525 ÷ 3 4 = 22 5 3131 ÷ Divide. Write the answer in simplest form. = 22 5 1313 7 15 = or 1 22 15 Check It Out! Example1B Rally Coach B

8. 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. 13.2 4 = 1.32 0.4 = 1.32 0.4 1 decimal place1 zero 10 Notes

9. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Find 0.384 ÷ 0.24. 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. 0.24 ) 0.384 24 ) 38.4 Then divide as a whole number. 1  24 144.6 0.384 ÷ 0.24 = 1.6 Estimate: 40 ÷ 20 = 2 The answer is reasonable. – 144 0 Notes

10. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Find 0.65 ÷ 0.25. Estimate the reasonableness of your answer. Check It Out! Example 2 0.25 has two decimal places so multiple both numbers by 100 to make the divisor an integer. 0.25 ) 0.65 25 ) 65.0 Then divide as a whole number. 2  50 150.6 0.65 ÷ 0.25 = 2.6 Estimate: 60 ÷ 20 = 3 The answer is reasonable. –150 n 0 Elbow Partners

11. 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. 5.25 n 0.15 = When n = 0.15, = 35. 5.25 n 0.15 ) 5.25 0.15 has two decimal places, so multiply both numbers by 100 to make the divisor an integer.  525 0 15 ) 525 35 Notes

12. 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. 3.60 n 0.12 = When n = 0.12, = 30. 3.60 n 0.12 ) 3.60 0.12 has two decimal places, so multiply both numbers by 100 to make the divisor an integer.  360 0 12 ) 360 30 Face Partners

13. 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? 1616 5858 Numbers Understand the Problem Make a PlanSolveLook Back Notes