**Multiplication facts :**

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 fact of that operation.

Here, we are going to know the work done by the binary operation "Multiplication".

Let us consider the following example to understand the important fact 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 facts of multiplication : **

(i) Commutative property

(ii) Multiplication by zero

(iii) Associative property

(iv) Multiplicative identity

(v) Multiplicative inverse

(vi) Distributive property of multiplication

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.

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

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)

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

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 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 "Multiplication facts".

Apart from the stuff given above, if you want to know more about "Multiplication facts", please click here

Apart from "Multiplication facts", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**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**