PROPERTIES OF MULTIPLICATION
About "Properties of multiplication"
Properties of multiplication :
We have four binary operations in math. They are
Addition, Subtraction, Multiplication and Division
When we use each of the above binary operations, the result may be different.
It is because of the work done by the binary operation that we have between the two numbers. Knowing the work done by the binary operation is called the property of that operation.
Here, we are going to know the work done by the binary operation "Multiplication".
Properties of multiplication - Examples
Let us consider the following example to understand the important property of multiplication.
Example :
A teacher wants to gift $20 cash prize to one of the students for his performance in the class.
In case, if the teacher wants to gift the same cash prize $20 to six students, how much does he have to spend ?
To get answer for the above question, we will be writing 20 six times and add them all.
That is,
20 + 20 + 20 + 20 + 20 + 20
Adding 20 six times can be written as (6x20).
Here, the fact what we have to understand is, the result of adding 20 six times is equal to multiplying 6 and 20.
More clearly,
20+20+20+20+20+20 = 6x20 = 120
Therefore, to gift $20 cash prize to six students, the teacher has to spend $120.
Other properties of multiplication :
(i) Commutative property
(ii) Multiplication by zero
(iii) Associative property
(iv) Multiplicative identity
(v) Multiplicative inverse
(vi) Distributive property of multiplication
Commutative property
Observe the following :
5 × (– 6) = – 30 and (– 6) × 5 = – 30
Therefore, 5 × (– 6) = (– 6) × 5
Therefore, multiplication is commutative for all real numbers.
In general, for any two real numbers a and b, a × b = b × a.
Multiplication by zero
The product of any nonzero real number with zero is zero.
Observe the following:
5 × 0 = 0
– 8 × 0 = 0
In general, for any nonzero real number "a"
a × 0 = 0 × a = 0
Associative property
Consider the real numbers 2, – 5, 6.
Look at
[2 x (-5)] x 6 = -10 x 6 = -60 and
2 x [(- 5) x 6] = 2 x (-30) = -60
Thus [2 x (-5)] x 6 = 2 x [(- 5) x 6]
So we can say that real numbers are associative under multiplication.
In general, for any real numbers a, b, c,
(a × b) × c = a × (b × c)
Multiplicative identity
Observe the following:
5 x 1 = 5
1 x (- 7) = -7
This shows that ‘1’ is the multiplicative identity for real numbers.
In general, for any real number "a" we have
a x 1 = 1 x a = a
Multiplicative inverse
For any real number, say "a", the multiplicative inverse is its reciprocal.
That is, multiplicative inverse of "a" is 1/a
For example,
The multiplicative inverse of 5 is 1/5
The multiplicative inverse of 3 is 1/3
Note :
Multiplication of a number and its multiplicative inverse is always 1.
That is,
5 x 1/5 = 1
Distributive property of multiplication
Distributive property of multiplication over addition :
Consider the real numbers 12, 9, 7.
Look at
12 x (9 + 7) = 12 x 16 = 192
12 x (9 + 7) = 12 x 9 + 12 x 7 = 108 + 84 = 192
Thus 12 x (9 + 7) = (12 x 9) + (12 x 7)
In general, for any real numbers a, b, c.
a x (b + c) = (a x b) + (a x c).
Therefore, multiplication is distributive over addition.
Distributive property of multiplication over subtraction :
Consider the real numbers 12, 9, 7.
Look at
12 x (9 - 7) = 12 x 2 = 24
12 x (9 - 7) = 12 x 9 - 12 x 7 = 108 - 84 = 24
Thus 12 x (9 - 7) = (12 x 9) - (12 x 7)
In general, for any real numbers a, b, c.
a x (b - c) = (a x b) - (a x c).
Therefore, multiplication is distributive over subtraction.
After having gone through the stuff given above, we hope that the students would have understood "Properties of multiplication".
Apart from the stuff given above, if you want to know more about "Properties of multiplication", please click here
Apart from "Properties of multiplication", if you need any other stuff in math, please use our google custom search here.
WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
