3 8 Dividing by Decimals Warm Up Problem

3 -8 Dividing by Decimals Warm Up Problem of the Day Lesson Presentation Course 1

3 -8 Dividing by Decimals Warm Up Divide. 1. 2. 3. 4. 5. Course 1 4. 8 ÷ 2 16. 1 ÷ 7 0. 36 ÷ 3 25. 28 ÷ 4 6. 25 ÷ 5 2. 4 2. 3 0. 12 6. 32 1. 25

3 -8 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. Course 1 4. 5 0. 25 3 1 1. 5 2. 25 0. 75 9 0. 5

3 -8 Dividing by Decimals Learn to divide whole numbers and decimals by decimals. Course 1

3 -8 Dividing by Decimals Helpful Hint Multiplying the divisor and the dividend by the same number does not change the quotient. 42 ÷ 6 = 7 10 420 ÷ 60 = 7 10 4, 200 ÷ 600 = 7 Course 1

3 -8 Dividing by Decimals Additional Example 1 A: Dividing a Decimal by a Decimal Find each quotient. A. 5. 2 ÷ 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. Course 1 5. 2 x 10 = 52

3 -8 Dividing by Decimals Additional Example 1 B: Dividing a Decimal by a Decimal B. 61. 3 ÷ 0. 36 61. 3 36 6, 130. 000 Course 1 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 -8 Dividing by Decimals Additional Example 1 B Continued 1 70. 2 77 36 6, 130. 000 -36 253 252 10 -0 100 -72 280 -252 28 Course 1 Divide. __ 170. 277… = 170. 27 When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient.

3 -8 Dividing by Decimals Try This: Example 1 A Find each quotient. A. 4. 8 ÷ 1. 2 4. 8 4 12 48 -48 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. 2 x 10 = 12 Divide. Course 1 4. 8 x 10 = 48

3 -8 Dividing by Decimals Try This: Example 1 B B. 51. 2 ÷ 0. 24 51. 2 24 5120. 000 Course 1 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 -8 Dividing by Decimals Try This: Example 1 B Continued 2 13. 3 3 24 5, 120. 00 -48 32 24 80 -72 8 Course 1 Divide. __ 213. 33… = 213. 33 When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient.

3 -8 Dividing by Decimals Additional Example 2: Problem Solving Application After driving 216. 3 miles, the Yorks used 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. Course 1

3 -8 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 Multiply the divisor and dividend by 10. Think: 10. 5 x 10 = 105 10. 5 216. 3 x 10 = 2, 163 Place the decimal point in the quotient. Divide. The York family averaged 20. 6 miles per gallon. Course 1

3 -8 Dividing by Decimals 4 Look Back Use compatible numbers to estimate the quotient. 216. 3 ÷ 10. 5 220 ÷ 11 =20 The answer is reasonable since 20. 6 is close to the estimate of 20. Course 1

3 -8 Dividing by Decimals Try This: Example 2 After driving 191. 1 miles, the Changs used 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. Course 1

3 -8 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 Multiply the divisor and dividend by 10. Think: 10. 5 x 10 = 105 10. 5 191. 1 x 10 = 1, 911 Place the decimal point in the quotient. Divide. The York family averaged 18. 2 miles per gallon. Course 1

3 -8 Dividing by Decimals 4 Look Back Use compatible numbers to estimate the quotient. 191. 1 ÷ 10. 5 190 ÷ 10 = 19 The answer is reasonable since 18. 2 is close to the estimate of 19. Course 1

3 -8 Dividing Insert Lesson by Decimals Title Here Lesson Quiz Find each quotient. 1. 49 ÷ 0. 7 70 2. 21. 63 ÷ 2. 1 10. 3 3. 38. 43 ÷ 6. 1 6. 3 4. 16. 9 ÷ 5. 2 3. 25 5. John spent $13. 44 renting 4 videos for the weekend. What was the cost per video? $3. 36 Course 1