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DECIMALSUnderstanding Division
andDividing With Decimals
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• Remove all other thoughts from your mind.• Pay close attention.• Try all the examples.• Ignore all other distractions.
For Learning To Happen:
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This flat represents 1 whole.or 100 squares.
This rod represents 1/10or 10 squares.
This block represents 1/100or 1 square.
Understanding Division
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1.01 whole
0.1
0.01
1 tenth
1 hundredth
Understanding Division
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How many rods fit into a flat?Flat 10
Understanding Division
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How many blocks fit into a flat?
100
Flat
Understanding Division
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How many blocks fit into a rod?rod
10
Understanding Division
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What does 36 ÷ 4 really mean?How many 4’s does it take to make 36.
Or how many 4’s fit into 36?
Understanding Division
9
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What does 50 ÷ 5 really mean?How many 5’s does it take to make 50.
Or how many 5’s fit into 50?
Understanding Division
10
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What does 1.2 ÷ 0.1 mean?
How many one tenths does it take to make 1 whole and 2 tenths?
Understanding Division
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What does 1.2 ÷ 0.1 mean? How many 0.1’s fit to make 1.2?
10 1 1The answer is 12
How many rods are there?
Understanding Division
How many one tenths fit to make 1.2?
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What does 1.2 ÷ 0.1 mean? LOOK FOR A PATTERN:
1.2 ÷ 0.1
If we multiply both sides by 10
We get the problem 1 2 ÷ 0 1
Understanding Division
BOTH DIVISION PROBLEMS GIVE YOU THE SAME ANSWER!
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What does 1.02 ÷ 0.1 mean?
How many one tenths does it take to make 1 whole and 2 hundreds?
Understanding Division
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What does 1.02 ÷ 0.1 mean? How many 0.1’s fit to make 1.02?
The answer is 10.2
It takes ten full rods and two-tenths of another
10
.1
.1
How many rods fit into 1.02?
Understanding Division
How many one tenths fit to make 1.02?
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What does 1.02 ÷ 0.01 mean?
How many one hundredths does it take to make 1 whole and 2 hundreds?
Understanding Division
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What does 1.02 ÷ 0.01 mean? How many 0.01’s fit to make 1.02?
The answer is 102100
1
1
How many blocks are there?
Understanding Division
How many one hundredths fit to make 1.02?
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What does 1.02 ÷ 0.01 mean?
Notice the answer is the SAME for both problems!
LOOK FOR A PATTERN:1.02 ÷ 0.01
If we multiply both sides by 100
Then we get the problem 102 ÷ 01
Understanding Division
x 100 100 x = 102
= 102
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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24 2 = 12
There are many ways to write a division problem.
There are two symbols , /
24 / 2 = 12
Dividing With Decimals
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There are 2 types of division problems involving decimal points:
1.) NO decimal in the divisor
2.) YES Decimal in the divisor
Divisor Dividend
Divide 0.32 8
Divide 0.32 0.8
Dividing With Decimals
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TRICK FOR LONG DIVISION Dead Monkeys Smell Bad
ULTIPLY
IVIDE
UBTRACT
RING DOWN Daffodils Make Spring
Beautiful Dad Mom Sister Brother
Dividing With Decimals
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Divide 0.27 3
0.27 0.27 3
=
0.09
Dividing With Decimals
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Divide 0.27 3
3 0 . 27. 0
0 02 7
9
27 0
Divisor Dividend
Step 2: Move the decimal point in the dividend straight up into the quotient
Step 3: Divide as usual
Step 1: Write the problem in the long division format
TRICK: Dead Monkeys Smell Bad!
Dividing With Decimals
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Divide 0.14 2
0.14 0.14 2
=
0.07
Dividing With Decimals
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LOOK FOR A PATTERNWhen 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 atthe denominator. The number of decimal places represents the number of zeros after the 1 in the power of 10. 13.2
4=1.32
0.4= 1.32
0.4
1 decimal place 1 zero
1010
Dividing With Decimals
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Divide 0.352 ÷ 0.22
0.22 has two decimal places so multiply both numbers by 100 to make the divisor a whole number.
0.22 )0.352
22 )35.2
Then divide as usual.
1
- 22 32
.6
20
Dividing With Decimals
1
1
13
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Dividend Divisor
Divide 0.75 0.15 Step 2: Move the decimal point in the divisor to the far right of the divisor
Step 5: Divide as usual
Step 1: Write the problem in the traditional long division
015 0 75. 0
0 075
5
75 0
Step 3: Move the decimal point the SAME number of places in the dividendStep 4: Move the decimal point in the dividend straight up into the quotient
. .
Dividing With Decimals
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Divide 0.45 ÷ 0.25
0.25 has two decimal places so multiply both numbers by 100 to make the divisor a whole number.
0.25 )0.45
25 )45Then divide as usual.
1
- 25 0
8
– 2000
Dividing With Decimals
2
0
0
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THE END!!!
That’s All Folks!
Take out your Study Guide!
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NO decimal point in the divisor.
Divide 0.27 3
3 0. 27. 0
0 02 7
9
27 0
#8 Divisor Dividend
Step 2: Move the decimal point in the dividend straight up.
Step 3: Divide as usual
Step 1: Write the problem as long division.
TRICK: Dead Monkeys Smell Bad!
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Divide Decimals
Step 2: Make the divisor a whole number by moving the decimal point to the far right
Step 5: Divide
Step 1: Write as long division
Divide 0.42 0.6
0 6 0 4 2. 0
0 042
7
42 0
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
. .. .
#9Dividend Divisor
Yes, decimal point in the divisor.