Properties of Multiplication
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Properties of Multiplication
An easier insight into how problems are factored can be shown through the four properties of
multiplication.
The name commutative holds definition in the prefix of the word, commute, meaning to move
from place to place.The Commutative Property shows how two numbers in a multiplication
number will result in the same answer despite the order, 3*2=6 and 2*3=6.
Multiplication and addition both use the Commutative Property, for example: a+b=b+a and
a*b*c=b*c*a.An addition or multiplication problem may cite the Commutative Property, which
wil simply mean that it is okay to move numbers around.
The Associative Property is named for associating or grouping and is also used in addition
and multiplication.The Associative Property states the irrelevance of number order within a
group of numbers that are multiplied or summed.
In the example, a(cb)=c(ba) and a+(c+b)=b+(a+c), the Associative Property is demonstrated.
Only the order of numbers would be need to be regrouped if a problem asked for
rearrangement through the Associative Property.
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Any number multiplied by one remains the same number, as stated by the Multiplicative
Identity Property.1*5=5 as well as 1*10=10as defined by this property.
The most complex of the four properties, the Distributive Property, is used to factor out a set of
numbers.The term distributive comes from the properties use of distribution of multiplication
over addition.
This property can be show through an example, such as: a(b+c)=ab+ac, and also as
ax+b=a(x+b).
This property can also be used for multiplication over subtraction as displayed in the example:
5x15=5(x3), in that the 5 is distributed to factor into parentheses just as it is factored out of
the parentheses.
Flexibility within the Distributive Property's definition is shown through the above example as
subtraction is used; subtraction can also be the addition of a negative number.
The examples and definitions of these four properties show how and why math rules are
used.Math skills are sharpened and ready for more complex quantitative problems once these
essentials of multiplication are understood.
Multiplication Methods
Below are the multiplication methods:
Method 1:
Multiplying integers of 345 x 6
Solution:
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Here, 5 is at unit place, so we do 5 x 1 = 5 x 6 = 30
4 is at 10's place, so we do 4 x 10 = 40 x 6 = 240
3 is at 100's place, so we do 3 x 100 = 300 x 6 = 1800
The product result = 2070
Method 2:
Multiplying integers of 345 x 6
Solution:
345
x 6

3 0
2 4 0
1 8 0 0

2 0 7 0

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