3-6 dividing by decimals warm up warm up lesson presentation lesson presentation problem of the day...
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3-6 Dividing by Decimals
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
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
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.
4.5 0.25
0.5
3
1 1.5 2.25
0.75 9
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
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
Additional Example 1A: 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
Additional Example 1B: Dividing a Decimal by a Decimal
61.3 ÷ 0.36
0.36 61.30
Think: 0.36 x 100 = 36 61.3 x 100 = 6,130
Multiply the divisor by 102, or 100, to make it a whole number. Multiply the dividend by the same power of 10.
36 6,130.000
3-6 Dividing by Decimals
Additional Example 1B Continued
Place the decimal point in the quotient. Divide as with whole numbers.
36 6,130.0007
-36
1
253-252
10 -0
0
100
.2
-72
-252
7
280-252
280
7
28 61.3 ÷ 0.36 = 170.27
__
When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient.
3-6 Dividing by Decimals
Check It Out: Example 1
Find the quotient.
51.2 ÷ 0.25
0.25 51.2 25 5120.00204.8
3-6 Dividing by Decimals
Additional Example 2: 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
Check It Out: Example 2
After driving 154.7 miles, the Changs filled up with 8.5 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 154.7 miles. They used 8.5 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
8.5 154.7
The Chang family averaged 18.2 miles per gallon.
3-6 Dividing by Decimals
Look Back44
Use compatible numbers to estimate the quotient.
154.7 ÷ 8.5 → 160 ÷ 8 = 20
The answer is reasonable because 18.2 is close to the estimate of 20.
3-6 Dividing by Decimals
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
3-6 Dividing by Decimals
Lesson Quiz
Find each quotient.
1. 49 ÷ 0.7
2. 21.63 ÷ 2.1
3. 38.43 ÷ 6.1
4. 16.9 ÷ 5.2
5. John spent $13.44 renting 4 videos for the
weekend. What was the cost per video?
10.3
70
6.3
3.25
$3.36
3-6 Dividing by Decimals
1. Identify the quotient.
72 0.9
A. 70
B. 79
C. 80
D. 90
Lesson Quiz for Student Response Systems
3-6 Dividing by Decimals
2. Identify the quotient.
36.12 4.2
A. 8.6
B. 8.8
C. 9.5
D. 9.6
Lesson Quiz for Student Response Systems
3-6 Dividing by Decimals
3. Identify the quotient.
51.51 5.1
A. 10.1
B. 10
C. 5.1
D. 5
Lesson Quiz for Student Response Systems
3-6 Dividing by Decimals
4. Identify the quotient.
26.35 6.2
A. 4.25
B. 4.5
C. 4.75
D. 5
Lesson Quiz for Student Response Systems