# Division of Literals

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

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