Dividing by Decimals

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

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

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

Remember! Quotient 0.15 5 0.75 Divisor Dividend

Terminating vs. Repeating Decimal What is a terminating decimal? What is a repeating decimal?

Terminating vs. Repeating Decimal What is a terminating decimal? What is a repeating decimal? A terminating decimal is one that terminates or ends.

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.

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.

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

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

Let’s try some multiplying and dividing shortcuts:

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 = 0.001 x 8.3 = 10,000 x 8.3 = 0.0001 x 8.3 =

Complete the table below: Whole Number Powers of 10 Decimal 10 x 8.3 = 83 0.1 x 8.3 = 100 x 8.3 = 830 0.01 x 8.3 = 1,000 x 8.3 = 8,300 0.001 x 8.3 = 10,000 x 8.3 = 83,000 0.0001 x 8.3 =

Complete the table below: Whole Number Powers of 10 Decimal 10 x 8.3 = 83 0.1 x 8.3 = 0.83 100 x 8.3 = 830 0.01 x 8.3 = 0.083 1,000 x 8.3 = 8,300 0.001 x 8.3 = 0.0083 10,000 x 8.3 = 83,000 0.0001 x 8.3 = 0.00083

What do you notice about the decimal point when you multiply by whole number powers of 10? Of decimal powers of 10?

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. 3.995 x 100 = 3 9 9. 5   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 0.001 = 0.3 9 9 5

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

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 = 0 . 3 5    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 ÷ 0.001 = 3 5 0 0 0 .

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

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. 1.3 5.2 4 Think: 1.3 x 10 = 13 5.2 x 10 = 52 13 52 Divide as with whole numbers. –52 5.2 ÷ 1.3 = 4

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. 0.24 51.2 Think: 0.24 x 100 = 24 51.2 x 100 = 5,120 24 5120.00

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 __

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

Understand the Problem Problem Solving Application After driving 216.3 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 216.3 miles. They used 10.5 gallons of gas.

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 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 as with whole numbers. -210 63 -0 630 -630 The York family averaged 20.6 miles per gallon.

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

John spent $13. 44 renting 4 videos for the weekend John spent $13.44 renting 4 videos for the weekend. What was the cost per video?

John spent $13. 44 renting 4 videos for the weekend John spent $13.44 renting 4 videos for the weekend. What was the cost per video? $3.36