# Division of Literals

Division of literals obeys all operation of division of numbers.

In arithmetic, we have studied that the division sign ‘÷’ read as ‘by’ between two numbers means that the number on the left of the division sign is to be divided by the number on the right.

For example:

15 ÷ 3 means that the number 15 on the left of the division sign is to be divided by the number 3 on the right of division sign.

In the case of literal numbers also x ÷ y read as ‘x by y’ means that the literal x is to be divided by the literal y and is written as x/y.

Thus 25 divided by a is written as 25/a and y divided by 5 written as y/5. It should be noted that 1/5 of y or y divided by 5 is also written as y/5.

Similarly, x divided by 10 is x/10. Quotient of 5 by z is 5/z.

Examples on Division of Literals:

Write each of the following phrases using numbers, literals and the basic operations of addition, subtraction, multiplication and division:

1. Quotient of x by 4 is added to y.

Solution: We have,

Quotient of x by 4 = x/4

Therefore, quotient of x by 4 added to y = x/4 + y

2. Quotient of z by 6 is multiplied by y.

Solution: We have,

Quotient of z by 6 = z/6

Therefore, quotient of z by 6 is multiplied by y = z/6 × y = zy/6

3. Quotient of x by y added to the product of x and y.

Solution: We have,

Question of x by y = x/y

And product of x and y = xy

Therefore, quotient of x by y and to product of x and y = x/y + xy.

4. 100 taken away from the quotient of 5m by 2x.

Solution: We have,
Quotient of 5m by 2x = 5m/2x.

Therefore, 100 taken away from the quotient of 5m by 2x = 5m/2x - 100

5. Product of 4 and a divided by the difference of 5 and a.

Solution: Product of 4 and a = 4a

Difference of 5 and a = (5 - a)

Thus, we have 4a ÷ (5 - a)

or, 4a/(5 - 4)

6. Express the share of each child algebraically if x apples were equally distributed among four children.

Solution: Total number of Apple = x

Number of children = 4

Therefore, each children gets x ÷ 4 = x/4 apples.

7. Quotient of x by 2 subtracted from 10 less than x

Solution: We have,

Quotient of x by 2 = x/2

10 less than x = (x - 10)

Thus, we have (x - 10) - x/2

Properties of Division of Literals

For any literal number a

(i) a ÷ a = 1

(ii) 0 ÷ a = 0

(iii) a ÷ 1 = a

Division of literals is neither commutative nor associative.