Transcript 3-5 - TeacherWeb

Dividing Decimals and
3-5 Integers by Decimals
Warm Up
Problem of the Day
Lesson Presentation
Course 2
Dividing Decimals and
3-5 Integers by Decimals
Warm Up
Divide.
1. 24.5 ÷ 7
3.5
2. 50.4 ÷ 6
8.4
3. 19.2 ÷ (–2)
–9.6
4. 128.1 ÷ 21
6.1
Course 2
Dividing Decimals and
3-5 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
Course 2
Dividing Decimals and
3-5 Integers by Decimals
Learn to divide decimals and integers by
decimals.
Course 2
Dividing Decimals and
3-5 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.
Course 2
Dividing Decimals and
3-5 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.
Course 2
Dividing Decimals and
3-5 Integers by Decimals
Additional Example 1A: Dividing Decimals by
Decimals
Divide.
8.28 ÷ 4.6
8.28 ÷ 4.6 = 82.8 ÷ 46
1.8
46) 82.8
– 46
36 8
–36 8
Multiply both numbers by 10 to
make the divisor an integer.
Divide as with whole numbers.
0
Helpful Hint
Multiply both numbers by the least power of ten that will
make the divisor an integer.
Course 2
Dividing Decimals and
3-5 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 0.5 6
Use zeros as placeholders
175 ) 1848 . 00
Divide as with whole
–175
numbers.
98 0
–87 5
10 50
–10 50
0
18.48 ÷ (–1.75) = –10.56
Course 2
The signs are different.
Dividing Decimals and
3-5 Insert
Lesson
Title Here
Integers
by Decimals
Check It Out: Example 1A
Divide.
6.45 ÷ 0.5
6.45 ÷ 0.5 = 64.5 ÷ 5
12 . 9
5 ) 64.5
–5
14
–10
45
–4 5
0
Course 2
Multiply both numbers by 10 to
make the divisor an integer.
Divide as with whole numbers.
Dividing Decimals and
3-5 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
8
integer.
206)1,648
–1 648
Divide as with whole
0
numbers.
16.48 ÷ (–2.06) = –8
Course 2
The signs are different.
Dividing Decimals and
3-5 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
3. 2
125 )400 .0
–375
25 0
–25 0
0
Estimate
4÷1=4
Course 2
Multiply both numbers by 100.
Use zero as a placeholder.
Divide as with whole numbers.
The answer is reasonable.
Dividing Decimals and
3-5 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)
9. 6
25 ) 240 .0
– 225
15 0
– 15 0
0
Estimate
–24 ÷ (–3) = 8
Course 2
Multiply both numbers by 10.
Divide as with whole numbers.
The answer is reasonable.
Dividing Decimals and
3-5 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
4.8
125 ) 600 .0
–500
100 0
–100 0
0
Estimate
6÷1=6
Course 2
Multiply both numbers by 100.
Use zero as a placeholder.
Divide as with whole numbers.
The answer is reasonable.
Dividing Decimals and
3-5 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)
8. 8
25 ) 220 .0
–200
20 0
–20 0
0
Estimate
–21 ÷ (–3) = 7
Course 2
Multiply both numbers by 10.
Divide as with whole numbers.
The answer is reasonable.
Dividing Decimals and
3-5 Integers by Decimals
Additional Example 3: Transportation Application
Eric paid $229.25 to rent a car. The fee to rent
the car was $32.75 per day. For how long did
Eric rent the car?
229.25 ÷ 32.75 = 22,925 ÷ 3,275
7
3,275 ) 22,975
–22,975
0
Eric rented the car for 7 days.
Course 2
Multiply both numbers
by 100.
Divide as with
whole numbers.
Dividing Decimals and
3-5 Insert
Lesson
Title Here
Integers
by Decimals
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
28
125) 3500
–250
1000
–1000
0
Multiply both numbers by 100.
Divide as with whole numbers.
Helpful Hint
To calculate miles per gallon, divide the
number of miles driven by the number
of gallons of gas used.
Jace’s truck’s gas mileage was 28 miles per gallon.
Course 2
Dividing Decimals and
3-5 Integers
Insert Lesson
Title Here
by Decimals
Lesson Quiz
Divide. Estimate to check whether each
answer is reasonable.
1. 78.2 ÷ 0.04
1,995
2. –9.72 ÷ 2.7
–3.6
3. 18.88 ÷ 1.6
11.8
4. 19.5 ÷ 3.25
6
5. Jordan used 32.46 gallons of gas to drive his
van 584.28 miles. How many miles did Jordan get
per gallon? 18
Course 2