Transcript 3-6
3-6 Dividing by Decimals Learn to divide whole numbers and decimals by decimals. 3-6 Dividing by Decimals Helpful Hint 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 3-6 Dividing by Decimals Additional Example 1A: Dividing a Decimal by a Decimal Find the quotient. 5.2 ÷ 1.3 1.3 5.2 4 13 52 –52 0 Multiply the divisor and dividend by the same power of ten. There is one decimal place in the divisor. Multiply by 101, or 10. Think: 1.3 x 10 = 13 Divide. 5.2 ÷ 1.3 = 4 5.2 x 10 = 52 3-6 Dividing by Decimals Additional Example 1B: Dividing a Decimal by a Decimal 61.3 ÷ 0.36 0.36 61.30 36 6,130.000 Make the divisor a whole number by multiplying the divisor and dividend by 102, or 100. Think: 0.36 x 100 = 36 61.3 x 100 = 6,130 3-6 Dividing by Decimals Additional Example 1B Continued 1 70.2 77 36 6,130.000 -36 253 -252 10 -0 100 -72 280 -252 280 -252 28 Place the decimal point in the quotient. Divide. When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient. __ 61.3 ÷ 0.36 = 170.27 3-6 Dividing by Decimals Check It Out: Example 1A Find the quotient. 6.6 ÷ 1.1 1.1 6.6 6 11 66 -66 0 Multiply the divisor and dividend by the same power of ten. There is one decimal place in the 1 divisor. Multiply by 10 , or 10. Think: 1.1 x 10 = 11 Divide. 6.6 ÷ 1.1 = 6 6.6 x 10 = 66 3-6 Dividing by Decimals Check It Out: Example 1B 51.2 ÷ 0.24 0.24 51.2 0 24 5120.00 Make the divisor a whole number by multiplying the divisor and dividend by 102, or 100. Think: 0.24 x 100 = 24 51.2 x 100 = 5,120 3-6 Dividing by Decimals Check It Out: Example 1B Continued 2 13.3 3 24 5,120.00 -48 32 -24 80 -72 80 -72 80 -72 8 Divide. When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient. __ 51.2 ÷ 0.24 = 213.3 3-6 Dividing by Decimals 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. 3-6 Dividing by Decimals 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. 3 Solve First estimate the answer. You can use compatible numbers. 216.3 ÷ 10.5 200 ÷ 10 = 20 3-6 Dividing by Decimals 3 Solve Continued 10.5 216.3 2 0.6 105 2163.0 -210 63 -0 630 -630 0 Multiply the divisor and dividend by 10. Think: 10.5 x 10 = 105 216.3 x 10 = 2,163 Place the decimal point in the quotient. Divide. The York family averaged 20.6 miles per gallon. 3-6 Dividing by Decimals 4 Look Back The answer is reasonable since 20.6 is close to the estimate of 20. 3-6 Dividing by Decimals 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. 3-6 Dividing by Decimals 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. 3 Solve First estimate the answer. You can use compatible numbers. 191.1 ÷ 10.5 190 ÷ 10 = 19 3-6 Dividing by Decimals 3 Solve Continued 10.5 191.1 1 8.2 105 1911.0 -105 861 -840 210 -210 0 Multiply the divisor and dividend by 10. Think: 10.5 x 10 = 105 191.1 x 10 = 1,911 Place the decimal point in the quotient. Divide. The Chang family averaged 18.2 miles per gallon. 3-6 Dividing by Decimals 4 Look Back The answer is reasonable since 18.2 is close to the estimate of 19.