Solving Decimal Division Problems with Positive and Negative Integers

1. California Standards Extension of NS2.3 Solve addition, subtraction, multiplication,and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.

2. You can use a grid to model 0.6  0.3. Circle groups of 0.3 and count the number of groups. There are 2 groups of 0.3 in 0.6, so 0.6 ÷ 0.3 = 2.

3. When you divide two numbers, you can multiply both numbers bythe same power of ten without changing the final answer. Multiply both 0.6 and 0.3 by 10: and 0.6  10 = 6 0.3 10 = 3 and 6÷ 3 = 2 0.6 ÷ 0.3 =2 By multiplying both numbers by the same power of ten, you can make the divisor an integer. Dividing by an integer is much easier than dividing by a decimal.

4. Helpful Hint Multiply both numbers by the least power of ten that will make the divisor an integer. Example 1A: Dividing Decimals by Decimals Divide. 8.28 ÷ 4.6 Multiply both numbers by 10 to make the divisor an integer. 8.28 ÷ 4.6 1. 8 Divide as with whole numbers. ) 82.8 46 46 – 36 8 –36 8 0

5. Example 1B: Dividing Decimals by Decimals Divide. 18.48 ÷ (–1.75) 18.48 ÷ (–1.75) Multiply both numbers by 100 to make the divisor an integer. 1 0 .5 6 Use zeros as placeholders. ) . 00 175 1848 Divide as with whole numbers. –175 0 9 8 –87 5 10 50 –10 50 0 The signs are different. 18.48 ÷ (–1.75) = –10.56

6. Example 2A: Dividing Integers by Decimals Divide. Estimate to check whether each answer is reasonable. 4 ÷ 1.25 4.00 ÷ 1.25 Multiply both numbers by 100. . 3 2 ) 125 Use zero as a placeholder. 400 .0 –375 Divide as with whole numbers. 25 0 –25 0 0 Estimate The answer is reasonable. 4 ÷ 1 = 4

7. Example 2B:Dividing Integers by Decimals Divide. Estimate to check whether each answer is reasonable. –24 ÷ (–2.5) Multiply both numbers by 10. –24.0 ÷ (–2.5) 9 6 . ) 0 240 . Divide as with whole numbers. 25 – 225 0 15 – 15 0 0 –24 ÷ (–2.5) = 9.6 The signs are the same. Estimate –24 ÷ (–3) = 8 The answer is reasonable.

8. Example 3: Transportation Application Eric paid $229.25 to rent a car. The fee to rent the car was $32.75 per day. For how long did Eric rent the car? 229.25 ÷ 32.75 Multiply both numbers by 100 to make the divisor an integer. 7 ) 22,925 3,275 Divide as with whole numbers. –22,925 0 Eric rented the car for 7 days.

9. Check It Out! Example 1A Divide. 6.45 ÷ 0.5 6.45 ÷ 0.5 Multiply both numbers by 10 to make the divisor an integer. 1 2 9 . ) 5 Divide as with whole numbers. 64.5 5 – 14 –10 4 5 –4 5 0

10. Check It Out! Example 2B Divide. Estimate to check whether each answer is Reasonable. –22 ÷ (–2.5) Multiply both numbers by 10. –22.0 ÷ (–2.5) 8 8 . ) 0 220 . Divide as with whole numbers. 25 –200 0 20 –20 0 0 Estimate –21 ÷ (–3) = 7 The answer is reasonable.

11. Helpful Hint To calculate miles per gallon, divide the number of miles driven by the number of gallons of gas used. Check It Out! Example 3 Jace took a trip in which he drove 350 miles. During the trip his truck used 12.5 gallons of gas. What was his truck’s gas mileage? 350.0 ÷ 12.5 Multiply both numbers by 10. 2 8 Divide as with whole numbers. ) 125 3500 –250 100 0 –1000 0 The gas mileage was 28 miles per gallon.