Learn to divide whole numbers and decimals by decimals.

Multiplying the divisor and the dividend by the same number does not change the quotient. 42 ÷ 6 = 7 10  10 420 ÷ 60 = 7  10  10 4,200 ÷ 600 = 7 Helpful Hint

Additional Example 1A: Dividing a Decimal by a Decimal Find the quotient. 5.2 ÷ 1.3 Multiply the divisor and dividend by the same power of ten. 1.3 5.2 4 There is one decimal place in the divisor. Multiply by 101, or 10. Think: 1.3 x 10 = 13 5.2 x 10 = 52 13 52 –52 Divide. 5.2 ÷ 1.3 = 4

Additional Example 1B: Dividing a Decimal by a Decimal 61.3 ÷ 0.36 Make the divisor a whole number by multiplying the divisor and dividend by 102, or 100. 0.36 61.30 Think: 0.36 x 100 = 36 61.3 x 100 = 6,130 36 6,130.000

Additional Example 1B Continued 7 .2 7 7 36 6,130.000 Place the decimal point in the quotient. Divide. -36 253 -252 10 -0 When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient. 100 -72 280 -252 280 61.3 ÷ 0.36 = 170.27 __ -252 28

Multiply the divisor and dividend by the same power of ten. 1.1 6.6 Check It Out: Example 1A Find the quotient. 6.6 ÷ 1.1 Multiply the divisor and dividend by the same power of ten. 1.1 6.6 6 There is one decimal place in the divisor. Multiply by 10 , or 10. Think: 1.1 x 10 = 11 6.6 x 10 = 66 1 11 66 -66 Divide. 6.6 ÷ 1.1 = 6

Check It Out: Example 1B 51.2 ÷ 0.24 Make the divisor a whole number by multiplying the divisor and dividend by 102, or 100. 0.24 51.2 Think: 0.24 x 100 = 24 51.2 x 100 = 5,120 24 5120.00

Check It Out: Example 1B Continued 2 1 3 .3 3 24 5,120.00 Divide. -48 32 -24 80 -72 When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient. 80 -72 80 -72 8 51.2 ÷ 0.24 = 213.3 __

Understand the Problem Additional Example 2: Problem Solving Application After driving 216.3 miles, the York’s filled up with 10.5 gallons of gas. On average, how many miles did they drive per gallon of gas? 1 Understand the Problem The answer will be the average number of miles per gallon. List the important information: They drove 216.3 miles. They used 10.5 gallons of gas.

2 Make a Plan Solve a simpler problem by replacing the decimals in the problem with whole numbers. If they drove 10 miles using 2 gallons of gas, they averaged 5 miles per gallon. You need to divide miles by gallons to solve the problem. Solve 3 First estimate the answer. You can use compatible numbers. 216.3 ÷ 10.5 200 ÷ 10 = 20

3 Solve Continued Multiply the divisor and dividend by 10. Think: 10.5 x 10 = 105 216.3 x 10 = 2,163 10.5 216.3 2 .6 105 2163.0 Place the decimal point in the quotient. Divide. -210 63 -0 630 -630 The York family averaged 20.6 miles per gallon.

Look Back 4 The answer is reasonable since 20.6 is close to the estimate of 20.

Understand the Problem Check It Out: Example 2 After driving 191.1 miles, the Chang’s filled up with 10.5 gallons of gas. On average, how many miles did they drive per gallon of gas? 1 Understand the Problem The answer will be the average number of miles per gallon. List the important information: They drove 191.1 miles. They used 10.5 gallons of gas.

2 Make a Plan Solve a simpler problem by replacing the decimals in the problem with whole numbers. If they drove 10 miles using 2 gallons of gas, they averaged 5 miles per gallon. You need to divide miles by gallons to solve the problem. Solve 3 First estimate the answer. You can use compatible numbers. 191.1 ÷ 10.5 190 ÷ 10 = 19

3 Solve Continued Multiply the divisor and dividend by 10. Think: 10.5 x 10 = 105 191.1 x 10 = 1,911 10.5 191.1 1 8 .2 Place the decimal point in the quotient. Divide. 105 1911.0 -105 861 -840 210 -210 The Chang family averaged 18.2 miles per gallon.

Look Back 4 The answer is reasonable since 18.2 is close to the estimate of 19.