1. 3-5 Dividing Decimals and Integers by Decimals Warm Up
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. 3-5 Dividing Decimals and Integers by Decimals Warm Up Divide.
Course 2
3-5
Dividing Decimals and Integers by Decimals
Warm Up
Divide.
÷ 7
÷ 6
÷ (–2)
÷ 21
3.5
8.4
–9.6
6.1

3. 3-5 Dividing Decimals and Integers by Decimals Problem of the Day
Course 2
3-5
Dividing Decimals and Integers by Decimals
Problem of the Day
Place 20 pennies in a row on a table. Replace every fourth coin with a nickel. Now replace every third coin with a dime. Then replace every sixth coin with a quarter. What is the value of the 20 coins now on the table?
$1.35

4. 3-5 Learn to divide decimals and integers by decimals.
Course 2
3-5
Dividing Decimals and Integers by Decimals
Learn to divide decimals and integers by decimals.

5. 3-5 Dividing Decimals and Integers by Decimals
Course 2
3-5
Dividing Decimals and Integers by Decimals
How many groups of 0.3 are in 0.6?
This problem is equivalent to 0.6 ÷ 0.3. You can
use a grid to model this division by circling groups
of 0.3 and counting the number of groups.
There are 2 groups of 0.3 in 0.6, so 0.6 ÷ 0.3 = 2.

6. 3-5 Dividing Decimals and Integers by Decimals
Course 2
3-5
Dividing Decimals and Integers by Decimals
When you divide two numbers, you can multiply
both numbers by the same power of ten without
changing the final answer.
Multiply both 0.6 and 0.3 by 10:
0.6 · 10 = 6
and
0.3 · 10 = 3
0.6 ÷ 0.3 = 2
and
6 ÷ 3 = 2
By multiplying both powers by the same power of ten, you can make the divisor an integer. Dividing by an integer is much easier than dividing by a decimal.

7. Additional Example 1A: Dividing Decimals by Decimals
Course 2
3-5
Dividing Decimals and Integers by Decimals
Additional Example 1A: Dividing Decimals by Decimals
Divide.
8.28 ÷ 4.6
Multiply both numbers by 10 to make the divisor an integer.
8.28 ÷ 4.6
= 82.8 ÷ 46 1. 8 46 )
82.8
Divide as with whole numbers. – 46 36 8
–36 8
Multiply both numbers by the least power of ten that will make the divisor an integer.
Helpful Hint

8. Additional Example 1B: Dividing Decimals by Decimals
Course 2
3-5
Dividing Decimals and Integers by Decimals
Additional Example 1B: Dividing Decimals by Decimals
Divide.
18.48 ÷ (–1.75)
18.48 ÷ (–1.75) =
1848 ÷ 175
Multiply both numbers by 100 to make the divisor an integer. 1 .5 6
Use zeros as placeholders
175 )
1848 . 00
–175
Divide as with whole
numbers. 9 8
–87 5
10 50
–10 50
18.48 ÷ (–1.75) = –10.56
The signs are different.

9. Insert Lesson Title Here
Course 2
3-5
Dividing Decimals and Integers by Decimals
Insert Lesson Title Here
Check It Out: Example 1A
Divide.
6.45 ÷ 0.5
6.45 ÷ 0.5
= 64.5 ÷ 5
Multiply both numbers by 10 to make the divisor an integer. 1 2 . 9 5 )
64.5
Divide as with whole numbers. – 5 14
–10 4 5
–4 5

10. 3-5 Dividing Decimals and Integers by Decimals
Course 2
3-5
Dividing Decimals and Integers by Decimals
Check It Out: Example 1B
Divide.
16.48 ÷ (–2.06)
16.48 ÷ (–2.06) =
1648 ÷ (206)
Multiply both numbers by 100 to make the divisor an integer. 8
206 )
1,648
–1 648
Divide as with whole numbers.
16.48 ÷ (–2.06) = –8
The signs are different.

11. Additional Example 2A: Dividing Integers by Decimals
Course 2
3-5
Dividing Decimals and Integers by Decimals
Additional Example 2A: Dividing Integers by Decimals
Divide. Estimate to check whether each answer is reasonable.
4 ÷ 1.25
4.00 ÷ 1.25 =
400 ÷ 125
Multiply both numbers by 100. 3 . 2
125 )
400 .0
Use zero as a placeholder.
–375
Divide as with whole numbers.
25 0
–25 0
Estimate
4 ÷ 1 = 4
The answer is reasonable.

12. Additional Example 2B: Dividing Integers by Decimals
Course 2
3-5
Dividing Decimals and Integers by Decimals
Additional Example 2B: Dividing Integers by Decimals
Divide. Estimate to check whether each answer is Reasonable.
–24 ÷ (–2.5)
–24.0 ÷ (–2.5) =
–240 ÷ (–25)
Multiply both numbers by 10. 9 . 6 25 )
240 .
Divide as with whole numbers.
– 225 15
– 15 0
Estimate
–24 ÷ (–3) = 8
The answer is reasonable.

13. 3-5 Dividing Decimals and Integers by Decimals
Course 2
3-5
Dividing Decimals and Integers by Decimals
Check It Out: Example 2A
Divide. Estimate to check whether each answer is reasonable.
6 ÷ 1.25
6.00 ÷ 1.25 =
600 ÷ 125
Multiply both numbers by 100. 4 . 8
125 )
600 .0
Use zero as a placeholder.
–500
Divide as with whole numbers.
100 0
–100 0
Estimate
6 ÷ 1 = 6
The answer is reasonable.

14. 3-5 Dividing Decimals and Integers by Decimals
Course 2
3-5
Dividing Decimals and Integers by Decimals
Check It Out: Example 2B
Divide. Estimate to check whether each answer is Reasonable.
–22 ÷ (–2.5)
–22.0 ÷ (–2.5) =
–220 ÷ (–25)
Multiply both numbers by 10. 8 . 8 25 )
220 .
Divide as with whole numbers.
–200 20
–20 0
Estimate
–21 ÷ (–3) = 7
The answer is reasonable.

15. Additional Example 3: Transportation Application
Course 2
3-5
Dividing Decimals and Integers by Decimals
Additional Example 3: Transportation Application
Eric paid $ to rent a car. The fee to rent the car was $32.75 per day. For how long did Eric rent the car?
÷ =
22,925 ÷ 3,275
Multiply both numbers
by 100. 7 )
3,275
22,975
Divide as with
whole numbers.
–22,975
Eric rented the car for 7 days.

16. Insert Lesson Title Here
Course 2
3-5
Dividing Decimals and Integers by Decimals
Insert Lesson Title Here
Check It Out: Example 3
Jace took a trip in which he drove 350 miles. During the trip his truck used 12.5 gallons of gas. What was his truck’s gas mileage?
350.0 ÷ 12.5 =
3500 ÷ 125
Multiply both numbers by 100. 2 8
Divide as with whole numbers.
125 )
3500
–250
To calculate miles per gallon, divide the number of miles driven by the number of gallons of gas used.
Helpful Hint
100
–1000
Jace’s truck’s gas mileage was 28 miles per gallon.

17. Insert Lesson Title Here
Course 2
3-5
Dividing Decimals and Integers by Decimals
Insert Lesson Title Here
Lesson Quiz
Divide. Estimate to check whether each answer is reasonable.
÷ 0.04
2. –9.72 ÷ 2.7
÷ 1.6
÷ 3.25
5. Jordan used gallons of gas to drive his van miles. How many miles did Jordan get per gallon?
1,995
–3.6
11.8 6 18