3-6 Dividing by Decimals Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

3-6 Dividing by Decimals Warm Up Divide ÷ ÷ ÷ ÷

3-6 Dividing by Decimals Problem of the Day In the following magic square, is the product of the numbers in every row, column, and diagonal. Fill in the missing numbers

3-6 Dividing by Decimals Learn to divide whole numbers and decimals by decimals.

3-6 Dividing by Decimals Multiplying the divisor and the dividend by the same number does not change the quotient. 42 ÷ 6 = 7 10  ÷ 60 = 7  10  10 4,200 ÷ 600 = 7 Helpful Hint

3-6 Dividing by Decimals Additional Example 1A: Dividing a Decimal by a Decimal Find the quotient. 5.2 ÷ Multiply the divisor and dividend by the same power of ten. There is one decimal place in the divisor. Multiply by 10 1, or 10. Think: 1.3 x 10 = x 10 = 52 Divide – ÷ 1.3 = 4

3-6 Dividing by Decimals Additional Example 1B: Dividing a Decimal by a Decimal 61.3 ÷ Think: 0.36 x 100 = x 100 = 6,130 Make the divisor a whole number by multiplying the divisor and dividend by 10 2, or ,

3-6 Dividing by Decimals Additional Example 1B Continued Place the decimal point in the quotient. Divide. 36 6, ÷ 0.36 = __ When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient.

3-6 Dividing by Decimals Check It Out: Example 1A Find the quotient. 6.6 ÷ Multiply the divisor and dividend by the same power of ten. There is one decimal place in the divisor. Multiply by 10, or 10. Think: 1.1 x 10 = x 10 = 66 1 Divide ÷ 1.1 = 6

3-6 Dividing by Decimals Check It Out: Example 1B 51.2 ÷ Think: 0.24 x 100 = x 100 = 5,120 Make the divisor a whole number by multiplying the divisor and dividend by 10 2, or

3-6 Dividing by Decimals Check It Out: Example 1B Continued Divide. 24 5, ÷ 0.24 = __ When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient. 8

3-6 Dividing by Decimals Additional Example 2: Problem Solving Application After driving 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 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. Solve 3 First estimate the answer. You can use compatible numbers ÷ ÷ 10 = 20

3-6 Dividing by Decimals The York family averaged 20.6 miles per gallon Solve Continued Multiply the divisor and dividend by 10. Think: 10.5 x 10 = x 10 = 2,163 Place the decimal point in the quotient. Divide.

3-6 Dividing by Decimals Look Back4 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 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 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. Solve 3 First estimate the answer. You can use compatible numbers ÷ ÷ 10 = 19

3-6 Dividing by Decimals The Chang family averaged 18.2 miles per gallon. Solve Continued Multiply the divisor and dividend by 10. Think: 10.5 x 10 = x 10 = 1,911 Place the decimal point in the quotient. Divide.

3-6 Dividing by Decimals Look Back4 The answer is reasonable since 18.2 is close to the estimate of 19.

3-6 Dividing by Decimals Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

3-6 Dividing by Decimals Lesson Quiz Find each quotient ÷ ÷ ÷ ÷ John spent $13.44 renting 4 videos for the weekend. What was the cost per video? $3.36

3-6 Dividing by Decimals 1. Identify the quotient. 72  0.9 A. 70 B. 79 C. 80 D. 90 Lesson Quiz for Student Response Systems

3-6 Dividing by Decimals 2. Identify the quotient  4.2 A. 8.6 B. 8.8 C. 9.5 D. 9.6 Lesson Quiz for Student Response Systems

3-6 Dividing by Decimals 3. Identify the quotient  5.1 A B. 10 C. 5.1 D. 5 Lesson Quiz for Student Response Systems

3-6 Dividing by Decimals 4. Identify the quotient  6.2 A B. 4.5 C D. 5 Lesson Quiz for Student Response Systems

3-6 Dividing by Decimals 5. Dee bought 5 cups of iced tea for $4.85. What was the cost per cup? A. $0.66 B. $0.69 C. $0.95 D. $0.97 Lesson Quiz for Student Response Systems