Transcript Dividing With Decimals

DECIMALS
Understanding Division
and
Dividing With Decimals
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For Learning To Happen:
•Remove all other thoughts from your mind.
•Pay close attention.
•Try all the examples.
•Ignore all other distractions.
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Understanding Division
This block
represents 1/100
or 1 square.
This flat
represents 1 whole.
or 100 squares.
This rod
represents 1/10
or 10 squares.
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Understanding Division
0.01
1 hundredth
1.0
1 whole
0.1
1 tenth
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Understanding Division
Flat
10
How many rods fit into a flat?
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Understanding Division
100
Flat
How many blocks fit into a flat?
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Understanding Division
10
rod
How many blocks fit into a rod?
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Understanding Division
What does 36 ÷ 4 really mean?
How many 4’s does it take to make 36.
Or how many 4’s fit into 36?
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9
Understanding Division
What does 50 ÷ 5 really mean?
How many 5’s does it take to make 50.
Or how many 5’s fit into 50?
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10
Understanding Division
What does 1.2 ÷ 0.1 mean?
How many one tenths
does it take to make
1 whole and 2 tenths?
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Understanding Division
What does 1.2 ÷ 0.1 mean?
How many 0.1’s fit to make 1.2?
How many one
tenths fit to
make 1.2?
The answer is 12
How many rods are there?
10
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1 1
Understanding Division
What does 1.2 ÷ 0.1 mean?
LOOK FOR A PATTERN:
We get the
problem
1.2 ÷ 0.1
12÷01
If we multiply both sides by 10
BOTH DIVISION PROBLEMS GIVE
YOU THE SAME ANSWER!
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Understanding Division
What does 1.02 ÷ 0.1 mean?
How many one tenths
does it take to make
1 whole and 2 hundreds?
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Understanding Division
What does 1.02 ÷ 0.1 mean?
How many 0.1’s fit to make 1.02?
How many one
tenths fit to
make 1.02?
How many rods fit into 1.02?
.1
It takes ten full rods and
two-tenths of another
10
The answer is 10.2
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.1
Understanding Division
What does 1.02 ÷ 0.01 mean?
How many one hundredths
does it take to make
1 whole and 2 hundreds?
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Understanding Division
What does 1.02 ÷ 0.01 mean?
How many 0.01’s fit to make 1.02?
How many one
hundredths fit
to make 1.02?
The answer is 102
How many blocks are there?
1
100
1
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Understanding Division
What does 1.02 ÷ 0.01 mean?
LOOK FOR A PATTERN:
100 x 1.02 ÷ 0.01 x 100 = 102
Then we get
the problem 102 ÷ 01 = 102
If we multiply both sides by 100
Notice the answer is the SAME for both problems!
So to make decimal problems easier multiply
your decimals by powers of 10 to work with
whole numbers instead of decimals.
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Dividing With Decimals
There are many ways to write a
division problem.
There are two symbols
24  2 = 12
24 / 2 = 12
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, /
Dividing With Decimals
There are 2 types of division problems
involving decimal points:
1.) NO decimal in the divisor
Divide 0.32  8
2.) YES Decimal in the divisor
Divide 0.32  0.8
Divisor Dividend
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Dividing With Decimals
TRICK FOR LONG DIVISION
Dead Monkeys Smell Bad
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Daffodils Make Spring Beautiful
Dad
Mom Sister Brother
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R
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G
D
O
W
N
Dividing With Decimals
Divide 0.27  3
=
0.27
0.27  3
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0.09
Dividing With Decimals
Divisor Dividend
Divide 0.27  3
. 09
3 0. 27
00
27
27
0
Step 1: Write the problem
in the long division
format
Step 2: Move the decimal
point in the dividend
straight up into the
quotient
Step 3: Divide as usual
TRICK: Dead Monkeys Smell Bad!
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Dividing With Decimals
Divide 0.14  2
=
0.14
0.14  2
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0.07
Dividing With Decimals
LOOK FOR A PATTERN
When dividing a decimal by a decimal,
multiply both numbers by a power of 10 so
you can divide by a whole number.
To decide which power of 10 to multiply by, look at
the denominator. The number of decimal places
represents the number of zeros after the 1 in
the power of 10.
1.32 = 1.32 10 = 13.2
4
0.4
0.4 10
1 decimal place
1 zero
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Dividing With Decimals
Divide 0.352 ÷ 0.22
0.22 )0.352
1.6
1
22 )35.2
- 22
13 2
13 2
0
0.22 has two decimal places so
multiply both numbers by 100 to make
the divisor a whole number.
Then divide as usual.
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Dividing With Decimals
Dividend  Divisor
 0.15
0 5.
Divide 0.75
. 0 .75
015
00
75
75
0
Step 1: Write the problem in
the traditional long division
Step 2: Move the decimal point
in the divisor to the far right of
the divisor
Step 3: Move the decimal
point the SAME number of
places in the dividend
Step 4: Move the decimal
point in the dividend straight
up into the quotient
Step 5: Divide as usual
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Dividing With Decimals
Divide 0.45 ÷ 0.25
0.25 )0.45
1 8
25 )450
- 25
2 00
– 200
0
0.25 has two decimal places so
multiply both numbers by 100 to make
the divisor a whole number.
Then divide as usual.
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That’s All Folks!
THE END!!!
Take out your Study Guide!
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#8
NO decimal point in the divisor.
Divisor Dividend
Divide 0.27  3
Step 1: Write the problem
as long division.
. 09
Step 2: Move the decimal
3 0. 27
point in the dividend
00
straight up.
27
27
Step 3: Divide as usual
0
TRICK: Dead Monkeys Smell Bad!
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#9
Divide Decimals
Dividend  Divisor
Divide 0.42  0.6
Step 1: Write as long division
Yes, decimal point in the divisor. Step 2: Make the divisor a
0 .7
0 .6 . 0. 4 . 2
00
42
42
0
whole number by moving the
decimal point to the far right
Step 3: Inside the dividend
move the decimal point the
SAME NUMBER of places
Step 4: Move the decimal
point from the dividend
straight up
Step 5: Divide
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