 In your earlier classes, you might have learned how to divide one number with another number. Now through this Worksheet on Division of Literals, you will learn how to divide one literal with another literal. In algebra there arise two scenarios for dividing literals i.e. dividing literals of same, dividing different literals.

This Dividing Literals Worksheet includes questions for both the methods and is explained step by step for better understanding. Students will get numerous problems on the concept and answering them regularly helps them to master the concept as well.

Also, Read: Worksheet on Powers of Literal Numbers

Division of Literals Worksheet with Answers

I.  Write each of the following algebraically using signs and symbols:

(i) Quotient of m by y is multiplied by z.
(ii) Quotient of p by q added to the product of p and q.
(iii) 250 taken away from the quotient of 4m by 5n.
(iv) Product of 20 and m divided by the difference of p and 7.
(v) Quotient of b by k is added to s.
(vi) q was taken away from the quotient of 3p by 4s.

Solution:

(i) The quotient of m by y is m/y
The quotient of m by y multiplied by z is represented algebraically as mz/y.
(ii) The quotient of p by q is p/q
The product of p and q is pq
The quotient of p by q added to the product of p and q is represented algebraically as  p/q + pq.
(iii) The quotient of 4m by 5n is 4m/5n
250 taken away from the quotient of 4m by 5n is represented algebraically as   4m/5n – 250.
(iv) The Product of 20 and m is 20m
The difference between p and 7 is p-7
The Product of 20 and m divided by the difference of p and 7 are represented algebraically as 20m/(p – 7).
(v) The Quotient of b by k is b/k
The Quotient of b by k is added to s is represented algebraically as  b/k + s.
(vi) The quotient of 3p by 4s is 3p/4s
q taken away from the quotient of 3p by 4s has represented algebraically as 3p/4s – q.

II. Write each of the following statements using numbers, literals, and symbols:

(i) Quotient of m by 60 subtracted from 100 less than m.
(ii) Quotient of m by n added to the product of s and t.
(iii) Product of x and 40 divided by the difference of y and z.
(iv) Quotient of x by 3 multiplied by z.
(v) Quotient of 15 by k added to the product of 8 and l.
(vi) 5p taken away from the quotient of 7q by 9r.

Solution:

(i) Quotient of m by 60 is =m/60
The quotient of m by 60 subtracted from 100 less than m is represented algebraically as (m – 100) – m/60.
(ii) The quotient of m by n is m/n
The product of s and t is st
The quotient of m by n added to the product of p and q is represented algebraically as m/n+st.
(iii) The product of x and 40 is 40x
The difference between y and z is y-z
The product of x and 40 divided by the difference of y and z is represented algebraically as 40x/(y-z).
(iv) The quotient of x by 3 is x/3
The quotient of x by 3 multiplied by z is represented algebraically as  x/3*z=xz/3.
(v) The quotient of 15 by k  =15/k
the product of 8 and l = 8l
The quotient of 15 by k is added to the product of 8 and l is represented algebraically as 15/k+8l.
(vi) the quotient of 7q by 9r is 7q/9r
5p taken away from the quotient of 7q by 9r is represented algebraically as 7q/9r – 5p.

III. Write the following phrases algebraically:
(i) Quotient of x by 5 is added to y.
(ii) Quotient of ab by x is added to y.
(iii) 200 taken away from the quotient of 3p by 5q.
(iv) Product of a and b divided by the difference of m and n.
(v) Quotient of 13 by 5a added to the product of 17 and t.
(vi) Quotient of 40x by y is multiplied by l.

Solution:

(i) Quotient of x by 5 is added to y is represented algebraically as x/5+y.
(ii) Quotient of ab by x is added to y is represented algebraically as ab/x + y.
(iii) 200 taken away from the quotient of 3p by 5q is represented algebraically as 3p/5q – 200.
(iv) Product of a and b divided by the difference of m and n is represented algebraically as ab/m-n.
(v) Quotient of 13 by 5a added to the product of 17 and t is represented algebraically as 13/5a+17t.
(vi) Quotient of 40x by y is multiplied by l is represented algebraically as 40x/y*l=40xl/y.

IV. Express the share of the friends algebraically if x apples were equally distributed among three friends?

Solution:

Given that,
No. of apples=x
No. of friends=3
X apples were equally distributed among three friends=x/3
Hence, apples were distributed among three friends are represented algebraically as x/3.

V. Ram has K money. He wants to distribute the money to his two sons Rishi and Raghav. Express the share of the sons algebraically?

Solution:

Given that,
Total Money=k
No. of sons=2
Money was equally distributed to his two sons=k/2
Hence, Money was equally distributed to his two sons is represented algebraically as k/2.