Standards California 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. California Standards

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.

When you divide two numbers, you can multiply both numbers by the same power of ten without changing the final answer. Multiply both 0.6 and 0.3 by 10: 0.6  10 = 6 and 0.3  10 = 3 0.6 ÷ 0.3 = 2 and 6 ÷ 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.

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. 46 ) 82.8 – 46 36 8 –36 8 Multiply both numbers by the least power of ten that will make the divisor an integer. Helpful Hint

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 .5 6 Use zeros as placeholders. 175 ) 1848 . 00 –175 Divide as with whole numbers. 9 8 –87 5 10 50 –10 50 18.48 ÷ (–1.75) = –10.56 The signs are different.

Check It Out! Example 1B Divide. 16.48 ÷ (–2.06) 16.48 ÷ (–2.06) Multiply both numbers by 100 to make the divisor an integer. 8 206 ) 1,648 –1 648 Divide as with whole numbers. 16.48 ÷ (–2.06) = –8 The signs are different.

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 ) 400 .0 Use zero as a placeholder. –375 Divide as with whole numbers. 25 0 –25 0 Estimate 4 ÷ 1 = 4 The answer is reasonable.

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

Divide. Estimate to check whether each answer is reasonable. Check It Out! Example 2A Divide. Estimate to check whether each answer is reasonable. 6 ÷ 1.25 6.00 ÷ 1.25 Multiply both numbers by 100. 4 . 8 125 ) 600 .0 Use zero as a placeholder. –500 Divide as with whole numbers. 100 0 –100 0 Estimate 6 ÷ 1 = 6 The answer is reasonable.

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 3,275 ) 22,925 Divide as with whole numbers. –22,925 Eric rented the car for 7 days.

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 ) 64.5 Divide as with whole numbers. – 5 14 –10 4 5 –4 5

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

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 To calculate miles per gallon, divide the number of miles driven by the number of gallons of gas used. Helpful Hint 100 –1000 The gas mileage was 28 miles per gallon.