5.5 Dividing Signed Decimal Numbers Chapter 5 Rational Numbers: Positive and Negative Decimals

5.5 Dividing Signed Decimal Numbers Objectives Divide a decimal by an integer. Divide a number by a decimal. Estimate the answer when dividing decimals. Use the order of operations with decimals. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Objective 1: Divide a decimal by an integer. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.5 - 4

Objective 1: Divide a decimal by an integer. Find the quotient 21.93 ÷ (–3). Example First consider 21.93 ÷ 3. Step 1 Write the decimal point in the quotient directly above the decimal point in the dividend. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.5 - 5

Objective 1: Divide a decimal by an integer. Example (continued) Step 2 Divide as if the numbers were whole numbers. Check by multiplying the quotient times the divisor. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.5 - 6

Objective 1: Divide a decimal by an integer. Example (continued) Step 3 The quotient is –7.31 because the numbers have different signs. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.5 - 7

Objective 1: Divide a decimal by an integer. Example Find the quotient 470.7 ÷ 9. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.5 - 8

Objective 1: Divide a decimal by an integer. Example Divide 1.5 by 8. Use multiplying to check the quotient. Keep dividing until the remainder is 0, or until the digits in the quotient begin to repeat in a pattern. If you run out of digits in the dividend, write extra zeros on the right side of the dividend so you can continue dividing. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.5 - 9

Objective 1: Divide a decimal by an integer. Example (continued) Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.5 - 10

Objective 1: Divide a decimal by an integer. Example Divide 4.7 by 3. Round to the nearest thousandth. Write extra zeros in the dividend so that you can continue dividing. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.5 - 11

Objective 1: Divide a decimal by an integer. (continued) Example The digit 6 in the quotient is repeating and will continue to do so. The remainder will never be 0. The quotient is a repeating decimal that goes on forever. We may write the quotient in two ways. or Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.5 - 12

Objective 1: Divide a decimal by an integer. Example (continued) Check the answer by multiplying 1.567 by 3. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.5 - 13

Objective 2: Divide a number by a decimal. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.5 - 14

Objective 2: Divide a number by a decimal. Example Divide . Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.5 - 15

Objective 2: Divide a number by a decimal. Example Divide –5 by –4.2. Round to the nearest hundredth. First consider . Move the decimal point in the divisor one place to the right so that becomes the whole number 42. The decimal point in the dividend is also moved one place to the right. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.5 - 16

Objective 2: Divide a number by a decimal. Example (continued) Rounding the quotient to the nearest hundredth gives 1.19. The quotient is positive because both the divisor and dividend have the same sign. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.5 - 17

Objective 3: Estimate the answer when dividing by decimals. Example Suppose a student was asked to estimate the quotient 580.44 ÷ 2.8 using front end rounding and then find the exact answer. Find the error in the student’s solution that follows. The exact answer should be 207.3. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.5 - 18

Objective 4: Use the order of operations with decimals. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.5 - 19

Objective 4: Use the order of operations with decimals. Example Simplify using the order of operations. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.5 - 20

Objective 4: Use the order of operations with decimals. Example Simplify using the order of operations. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.5 - 21

Objective 4: Use the order of operations with decimals. Example Simplify using the order of operations. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.5 - 22