Multiplication with Decimals

1
Multiplication with Decimals
Reminder
Multiplying with the grid method
65 x 23
This can be re written as (60 5) x (20 3)
60
5
20
3
We now put this into the grid
Add the answers together
0
0
Multiply out the numbers to fill the grid
0
12
0
10
18
15
1495
2
Multiplication with Decimals
3
Multiplication with Decimals
To multiply decimals we use the same method, but
we have to think about the place value
To multiply as this is can cause confusion so we
think about the denomination
6.5 x 2.3
0.1 1 tenth
so 6.5 65 tenths
also 2.3 23 tenths
1.0 10 tenths
Therefore as long as we remember the denomination
we can multiply using the grid method
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Multiplication with Decimals
This answer was found by multiplying tenths x
tenths
60 5 20 3
100
1200
1 100
1 x 1 10 10
180
15

1495
1 100
So the denomination of the answer is
The numerical answer is 1495, so the place value
of the 5 is
1 100
Therefore the correct answer in denomination of
1s is
14.95
5
Multiplication with Decimals
We can check that the answer is correct by
estimating
Estimate to 7 x 3
14
6.5 x 2.3
Therefore we expect an answer about 14.
Inspect the answer 1495
If we put the decimal point here
1.495
the answer is clearly too small
If we put the decimal point here
149.5
the answer is clearly too big
The answer must be 14.95
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Multiplication with Decimals
7
Multiplication with Decimals
Points to note
What happens when you have a number less than 1
multiplied by another number less than 1?
0.1 is called a decimal fraction
because it is 1 written in decimal notation
10
Therefore 0.1 x 10 is finding 1 of 10 (a fraction
of a quantity)
10
0.1 x 10 1
Therefore 0.1 x 0.1 is finding 1 of 1
10 10
0.1 x 0.1 0.01
When a number less than 1 is squared the answer
is even smaller
Therefore 0.12 0.01
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Multiplication with Decimals
0.06
0.16
0.08
0.25
0.09
0.36
0.18
0.49
0.9
0.56
0.04
0.008
0.09
0.064