3-7 Dividing by Decimals Warm Up Problem of the Day Course 1 Warm Up Problem of the Day Lesson Presentation

3-7 Dividing by Decimals Warm Up Divide. 1. 4.8 ÷ 2 2. 16.1 ÷ 7 Course 1 3-7 Dividing by Decimals Warm Up Divide. 1. 4.8 ÷ 2 2. 16.1 ÷ 7 3. 0.36 ÷ 3 4. 25.28 ÷ 4 2.4 2.3 0.12 6.32

3-7 Dividing by Decimals Problem of the Day Course 1 3-7 Dividing by Decimals Problem of the Day In the following magic square, 3.375 is the product of the numbers in every row, column, and diagonal. Fill in the missing numbers. 4.5 0.25 0.5 3 1 1.5 2.25 0.75 9

Course 1 3-7 Dividing by Decimals Learn to divide whole numbers and decimals by decimals.

3-7 Dividing by Decimals Helpful Hint Course 1 3-7 Dividing 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 Course 1 3-7 Dividing by Decimals 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 Course 1 3-7 Dividing by Decimals 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 Course 1 3-7 Dividing by Decimals Additional Example 1B Continued 1 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

3-7 Dividing by Decimals Check It Out: Example 1A Find the quotient. Course 1 3-7 Dividing by Decimals 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

3-7 Dividing by Decimals Check It Out: Example 1B 51.2 ÷ 0.24 Course 1 3-7 Dividing by Decimals 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 Course 1 3-7 Dividing by Decimals 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 = 213.33 __

Understand the Problem Course 1 3-7 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.

3-7 Dividing by Decimals 2 Make a Plan Course 1 3-7 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. Solve 3 First estimate the answer. You can use compatible numbers. 216.3 ÷ 10.5 200 ÷ 10 = 20

3-7 Dividing by Decimals 3 Solve Continued Course 1 3-7 Dividing by Decimals 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.

3-7 Dividing by Decimals Look Back 4 Course 1 3-7 Dividing by Decimals Look Back 4 The answer is reasonable since 20.6 is close to the estimate of 20.

Understand the Problem Course 1 3-7 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.

3-7 Dividing by Decimals 2 Make a Plan Course 1 3-7 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. Solve 3 First estimate the answer. You can use compatible numbers. 191.1 ÷ 10.5 190 ÷ 10 = 19

3-7 Dividing by Decimals 3 Solve Continued Course 1 3-7 Dividing by Decimals 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.

3-7 Dividing by Decimals Look Back 4 Course 1 3-7 Dividing by Decimals Look Back 4 The answer is reasonable since 18.2 is close to the estimate of 19.

Insert Lesson Title Here Course 1 3-7 Dividing by Decimals Insert Lesson Title Here Lesson Quiz Find each quotient. 1. 49 ÷ 0.7 2. 21.63 ÷ 2.1 3. 38.43 ÷ 6.1 4. 16.9 ÷ 5.2 5. John spent $13.44 renting 4 videos for the weekend. What was the cost per video? 70 10.3 6.3 3.25 $3.36