Division of Literals

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In this section we will discuss about Division of Literals.

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, 18 ÷ 3 means that the number 18 on the left of the division is to be divided by the number 3 on the right side of division sign. In the case Division of Literals also a ÷ b read as ‘a by b’ means that the literal a is to be divided by the literal b and is written as a/b.

Thus, 20 divided by x is written as 20/x and x is divided by 3 is written as x/3. It should be noted that 1/3 of x or x is divided by 3 is also written as x/3

Examples:

1. Write each one of the following phrases by using numbers, literals and signs of basic operations:

(i) Quotient of x by 3 is multiplied by y
Solution :
We have, quotient of x by 3 = (x/3).(y)
= xy/3

(ii) 3 times x added to 7 by y
Solution :
We have, 3 times x = 3x, and 7 by y = 7/y.
∴ 3 times x added to 7 by (divided) y = 3x + 7/y.

(iii) Quotient of x by 4 is added to z
Solution:
We have, Quotient of x by 4 = x/4 + z

Write each of the following phrases by using numbers, literals and signs of basic operations :

(i) Quotient of z by 6 is multiplied by y.
Solution :
We have, Quotient of z by 6 = z/6
:. Quotient of z by 6 is multiplied by y means , z/6 x y = zy/6

(ii) Quotient of x by y added to the product of x and y
Solution :
We have, Quotient of x by y = x/y, and product of x and y = xy
∴ Quotient of x by y added to the product of x and y = x/y + xy

(iii) 4 taken away from the quotient of x by 2y.
Solution :
We have, Quotient of x by 2y = x/2y
∴ 4 taken away from the quotient of x by 2y = x/2y – 4

Introduction to Algebra