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3-6 Dividing by Decimals
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
3-6 Dividing by Decimals
Warm Up
Divide.
1. 4.8 ÷ 2
2. 16.1 ÷ 7
2.4
2.3
3. 0.36 ÷ 3
0.12
4. 25.28 ÷ 4
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
3
1
1.5
2.25
0.75
9
0.5
3-6 Dividing by Decimals
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
3-6 Dividing by Decimals
Helpful Hint
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
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
4
13 52
–52
0
5.2 ÷ 1.3 = 4
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.
3-6 Dividing by Decimals
Additional Example 1B: Dividing a Decimal by a
Decimal
61.3 ÷ 0.36
0.36 61.30
36 6,130.000
Multiply the divisor by 102, or
100, to make it a whole number.
Multiply the dividend by the same
power of 10.
Think: 0.36 x 100 = 36
61.3 x 100 = 6,130
3-6 Dividing by Decimals
Additional Example 1B Continued
1 70.2 77
36 6,130.000
-36
253
-252
10
-0
100
-72
280
-252
280
-252
28
Place the decimal point in
the quotient. Divide as with
whole numbers.
When a repeating pattern
occurs, show three dots or
draw a bar over the repeating
part of the quotient.
__
61.3 ÷ 0.36 = 170.27
3-6 Dividing by Decimals
Check It Out: Example 1
Find the quotient.
51.2 ÷ 0.25
0.25
51.2
204.8
25 5120.00
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?
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.
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.
3
Solve
First estimate the answer. You can use
compatible numbers.
216.3 ÷ 10.5
200 ÷ 10 = 20
3-6 Dividing by Decimals
3
Solve Continued
10.5 216.3
2 0.6
105 2163.0
-210
63
-0
630
-630
0
Multiply 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.
The York family averaged 20.6 miles per gallon.
3-6 Dividing by Decimals
4
Look Back
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?
1
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
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.
3
Solve
8.5
154.7
The Chang family averaged 18.2 miles per
gallon.
3-6 Dividing by Decimals
4
Look Back
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.