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Dividing by Decimals

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

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**Sunshine State Standards**

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

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Warm Up Divide. ÷ 2 ÷ 7 ÷ 3 ÷ 4 2.4 2.3 0.12 6.32

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Remember! Quotient 0.15 5 0.75 Divisor Dividend

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**Terminating vs. Repeating Decimal**

What is a terminating decimal? What is a repeating decimal?

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**Terminating vs. Repeating Decimal**

What is a terminating decimal? What is a repeating decimal? A terminating decimal is one that terminates or ends.

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**Terminating vs. Repeating Decimal**

What is a terminating decimal? What is a repeating decimal? A terminating decimal is one that terminates or ends. A repeating decimal is one that keeps going and repeats a pattern.

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**Terminating vs. Repeating Decimal**

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

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**Terminating vs. Repeating Decimal**

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

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**Can you list some common repeating decimals and their matching division problem?**

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**Let’s try some multiplying and dividing shortcuts:**

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**Complete the table below:**

Whole Number Powers of 10 Decimal 10 x 8.3 = 0.1 x 8.3 = 100 x 8.3 = 0.01 x 8.3 = 1,000 x 8.3 = x 8.3 = 10,000 x 8.3 = x 8.3 =

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**Complete the table below:**

Whole Number Powers of 10 Decimal 10 x 8.3 = 0.1 x 8.3 = 100 x 8.3 = 0.01 x 8.3 = 1,000 x 8.3 = 8,300 x 8.3 = 10,000 x 8.3 = 83,000 x 8.3 =

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**Complete the table below:**

Whole Number Powers of 10 Decimal 10 x 8.3 = 0.1 x 8.3 = 100 x 8.3 = 0.01 x 8.3 = 1,000 x 8.3 = 8,300 x 8.3 = 10,000 x 8.3 = 83,000 x 8.3 =

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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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**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 10. x = Multiplying by decimal powers of 10: Move the decimal point one place to the left for each decimal place in the decimal power of 10. 399.5 x =

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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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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 10. 35 ÷ 100 = Dividing by decimal powers of 10: Move the decimal one place to the right for each decimal place in the decimal power of 10. 35 ÷ =

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**Multiplying the divisor and the dividend by the same number does not change the quotient.**

42 ÷ 6 = 7 10 10 420 ÷ 60 = 7 10 4,200 ÷ 600 = 7 Helpful Hint

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**Dividing a Decimal by a Decimal**

Find the quotient. 5.2 ÷ 1.3 Multiply the divisor by 101, or 10 to make it a whole number. Multiply the dividend by the same power of 10. 4 Think: 1.3 x 10 = x 10 = 52 13 52 Divide as with whole numbers. –52 5.2 ÷ 1.3 = 4

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Check It Out: 51.2 ÷ 0.24 Multiply the divisor by 102, or 100, to make it a whole number. Multiply the dividend by the same power of 10. Think: 0.24 x 100 = x 100 = 5,120

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**Place the decimal point in the quotient. Divide as with whole numbers. **

Check It Out: 2 1 3 .3 3 24 5,120.00 Place the decimal point in the quotient. Divide as with whole numbers. -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 = 213.3 __

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**Make a Problem Solving Plan:**

1 Understand the Problem 2 Make a Plan Solve 3 Look Back 4

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**Understand the Problem**

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 gallons of gas.

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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 = 20

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3 Solve Continued Multiply the divisor and dividend by 10. Think: 10.5 x 10 = x 10 = 2,163 2 .6 Place the decimal point in the quotient. Divide as with whole numbers. -210 63 -0 630 -630 The York family averaged 20.6 miles per gallon.

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Look Back 4 The answer is reasonable since 20.6 is close to the estimate of 20.

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**John spent $13. 44 renting 4 videos for the weekend**

John spent $ renting 4 videos for the weekend. What was the cost per video?

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**John spent $13. 44 renting 4 videos for the weekend**

John spent $ renting 4 videos for the weekend. What was the cost per video? $3.36

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EXAMPLE 3 Dividing Mixed Numbers 1 3 6 5 6 –2 = 19 3 17 6 – = 19 3 6 17 – = 19 3 (– 6) 17 – 2 1 Multiply. Divide out common factor. 38 = 17 –, or 4 17.

EXAMPLE 3 Dividing Mixed Numbers 1 3 6 5 6 –2 = 19 3 17 6 – = 19 3 6 17 – = 19 3 (– 6) 17 – 2 1 Multiply. Divide out common factor. 38 = 17 –, or 4 17.

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