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3-6 Dividing by Decimals

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3-6 Dividing by Decimals Essential Question: How do operations with decimals compare to operations with whole numbers?

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3-6 Dividing by Decimals MA.6.A.1.3 Solve real-world problems involving…division of…decimals. Also MA.6.A.1.1, MA.6.A.1.2. MA.6.A.5.3 Sunshine State Standards

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

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3-6 Dividing by Decimals Divisor Quotient Remember! Dividend

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3-6 Dividing by Decimals What is a terminating decimal? What is a repeating decimal?

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3-6 Dividing by Decimals What is a terminating decimal? A terminating decimal is one that terminates or ends. What is a repeating decimal?

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3-6 Dividing by Decimals What is a terminating decimal? A terminating decimal is one that terminates or ends. What is a repeating decimal? A repeating decimal is one that keeps going and repeats a pattern.

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3-6 Dividing by Decimals What is a terminating decimal? A terminating decimal is one that terminates or ends. 1 ÷ 8 =.125 What is a repeating decimal? A repeating decimal is one that keeps going and repeats a pattern.

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3-6 Dividing by Decimals What is a terminating decimal? A terminating decimal is one that terminates or ends. 1 ÷ 8 =.125 What is a repeating decimal? A repeating decimal is one that keeps going and repeats a pattern. _ 1 ÷ 3 =.3

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3-6 Dividing by Decimals

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3-6 Dividing by Decimals

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3-6 Dividing by Decimals Complete the table below: Whole Number Powers of 10 Decimal Powers of x 8.3 =0.1 x 8.3 = 100 x 8.3 =0.01 x 8.3 = 1,000 x 8.3 =0.001 x 8.3 = 10,000 x 8.3 = x 8.3 =

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3-6 Dividing by Decimals Complete the table below: Whole Number Powers of 10 Decimal Powers of x 8.3 = x 8.3 = 100 x 8.3 = x 8.3 = 1,000 x 8.3 = 8, x 8.3 = 10,000 x 8.3 = 83, x 8.3 =

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3-6 Dividing by Decimals Complete the table below: Whole Number Powers of 10 Decimal Powers of x 8.3 = x 8.3 = x 8.3 = x 8.3 = ,000 x 8.3 = 8, x 8.3 = ,000 x 8.3 = 83, x 8.3 =

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3-6 Dividing by Decimals What do you notice about the decimal point when you multiply by whole number powers of 10? Of decimal powers of 10?

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3-6 Dividing by Decimals Multiplying by Powers of 10 Multiplying by whole number powers of 10: Move the decimal point one place to the right for each zero in the whole number power of x 100 = Multiplying by decimal powers of 10: Move the decimal point one place to the left for each decimal place in the decimal power of x =

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3-6 Dividing by Decimals What do you think will happen to the decimal point when you divide by whole number powers of 10? Of decimal powers of 10?

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3-6 Dividing by Decimals Dividing by Powers of 10 Dividing by whole number powers of 10: Move the decimal point one place to the left for each zero in the whole number power of ÷ 100 = Dividing by decimal powers of 10: Move the decimal one place to the right for each decimal place in the decimal power of ÷ =

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

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3-6 Dividing by Decimals Dividing a Decimal by a Decimal Find the quotient. 5.2 ÷ Multiply the divisor by 10 1, or 10 to make it a whole number. Multiply the dividend by the same power of 10. Think: 1.3 x 10 = x 10 = 52Divide as with whole numbers – ÷ 1.3 = 4

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3-6 Dividing by Decimals Check It Out: 51.2 ÷ Think: 0.24 x 100 = x 100 = 5,120 Multiply the divisor by 10 2, or 100, to make it a whole number. Multiply the dividend by the same power of

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3-6 Dividing by Decimals Check It Out: Place the decimal point in the quotient. Divide as with whole numbers. 24 5, ÷ 0.24 = __ When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient. 8

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3-6 Dividing by Decimals 1 Understand the Problem 2 Make a Plan Solve 3 Look Back 4 Make a Problem Solving Plan:

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3-6 Dividing by Decimals Problem Solving Application After driving miles, the Yorks 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.

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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

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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 as with whole numbers.

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3-6 Dividing by Decimals Look Back4 The answer is reasonable since 20.6 is close to the estimate of 20.

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3-6 Dividing by Decimals John spent $13.44 renting 4 videos for the weekend. What was the cost per video?

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

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