Dividing by Decimals
Post on 03-Jan-2016
101 Views
Preview:
DESCRIPTION
Transcript
3-6 Dividing by Decimals
Dividing by Decimals
3-6 Dividing by Decimals
Dividing by Decimals
Essential Question:
How do operations with decimals compare
to operations with whole numbers?
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
3-6 Dividing by Decimals
Warm UpDivide.
1. 4.8 ÷ 2
2. 16.1 ÷ 7
3. 0.36 ÷ 3
4. 25.28 ÷ 4
2.42.3
0.12
6.32
3-6 Dividing by Decimals
Divisor
Quotient
Remember!
0.150.755
Dividend
3-6 Dividing by Decimals
What is a terminating decimal?
What is a repeating decimal?
3-6 Dividing by Decimals
What is a terminating decimal?
A terminating decimal is one
that terminates or ends.
What is a repeating decimal?
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.
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.
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
3-6 Dividing by Decimals
3-6 Dividing by Decimals
3-6 Dividing by Decimals
Complete the table below:Whole Number
Powers of 10Decimal
Powers of 10
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 =
3-6 Dividing by Decimals
Complete the table below:Whole Number
Powers of 10Decimal
Powers of 10
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 =
3-6 Dividing by Decimals
Complete the table below:Whole Number
Powers of 10Decimal
Powers of 10
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
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?
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 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
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?
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 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 .
3-6 Dividing by Decimals
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
3-6 Dividing by Decimals
Dividing a Decimal by a Decimal
Find the quotient.
5.2 ÷ 1.3
1.3 5.2 Multiply the divisor by 101, or 10 to make it a whole number. Multiply the dividend by the same power of 10.
Think: 1.3 x 10 = 13 5.2 x 10 = 52
Divide as with whole numbers. 13 52
4
–520
5.2 ÷ 1.3 = 4
3-6 Dividing by Decimals
Check It Out:
51.2 ÷ 0.24
0.24 51.2
Think: 0.24 x 100 = 24 51.2 x 100 = 5,120
Multiply the divisor by 102, or 100, to make it a whole number. Multiply the dividend by the same power of 10.
24 5120.00
0
3-6 Dividing by Decimals
Check It Out:
Place the decimal point in the quotient. Divide as with whole numbers.
24 5,120.001
-48
2
32 -24
80-72
3
80
.3
-72
-72 80
3
51.2 ÷ 0.24 = 213.3__
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
11 Understand the Problem
22 Make a Plan
Solve33
Look Back 44
Make a Problem Solving Plan:
3-6 Dividing by Decimals
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?
11 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.
3-6 Dividing by Decimals
22 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.
Solve33
First estimate the answer. You can use compatible numbers.
216.3 ÷ 10.5 200 ÷ 10 = 20
3-6 Dividing by Decimals
The York family averaged 20.6 miles per gallon.
105 2163.0-210
2
63 -0630
-630
0
0
.6
Solve Continued33
10.5 216.3Multiply the divisor and dividend by 10. Think: 10.5 x 10 = 105 216.3 x 10 = 2,163
Place the decimal point in the quotient. Divide as with whole numbers.
3-6 Dividing by Decimals
Look Back44
The answer is reasonable since 20.6 is close to the estimate of 20.
3-6 Dividing by Decimals
John spent $13.44
renting 4 videos for
the weekend. What
was the cost per
video?
3-6 Dividing by Decimals
John spent $13.44
renting 4 videos for
the weekend. What
was the cost per
video?
$3.36
top related