Definition of Coefficient:

Any factor or group of factors of a product is known as the coefficient of remaining factors.

**For example:**

In product 6mxy,

6 is the coefficient of mxy,

6x is the coefficient of my,

xy is the coefficient of 6m,

mxy is the coefficient of 6 and so on…….

**Note:** In the term 'm', the coefficient of m is 1 since 1 times m is equal to m. Similarly, in the term '-m' the coefficient of m is -1 since -1 times m is equal to -m.

If a factor is a numerical quantity, it is called numeral coefficient of
remaining factors and if the factor involves letters, it is called the
literal coefficient of remaining factors.

**For example:**

**(i) In product 11xy, we get;**

11 is numerical coefficient of xy,

x is literal coefficient of 11y,

xy is literal coefficient of 11,

y is literal coefficient of 11x

11y is literal coefficient of x and so on…….

**(ii) In product -7ab,**** we get;**

-7 is numerical coefficient of ab,

a is literal coefficient of -7b,

ab is literal coefficient of -7,

b is literal coefficient of -7a

-7b is literal coefficient of a and so on…….

3 is numerical coefficient of m

m

m

n is literal coefficient of 3m

3n is literal coefficient of m

**Write the coefficient of 'a' in each of the following:**

(i) 5a

(ii) 5/2ab(iii) a

(iv) -a

(v) 9abc

(vi) -7ax

**Solution:**

(i) 5a

The coefficient of a is 5

(ii) 5/2abThe coefficient of a is 5/2b

(iii) a

The coefficient of a is 1 [Since a = 1 ∙ a]

(iv) -a

The coefficient of a is -1 [Since -a = -1 ∙ a]

(v) 9abc

The coefficient of a is 9bc

(vi) -7ax

The coefficient of a is -7x

**● ****Coefficient - Worksheet**

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