Writing algebraic expressions from word problems worksheet with answers pdf

The following table will help you to learn some of the words (phrases) that can be used to indicate mathematical operations :

Question 1 :

Write the algebraic expressions for the following :

Sum of x and twice y

Question 2 :

Write the algebraic expressions for the following :

Subtraction of z from y

Question 3 :

Write the algebraic expressions for the following :

Twice the sum of m and n

Question 4 :

Write the algebraic expressions for the following :

b is  decreased by twice a

Question 5 :

Write the algebraic expressions for the following :

Sum of x squared and y squared

Question 6 :

Write the algebraic expressions for the following :

Two times the product of a and b divided by 5

Question 7 :

Write the algebraic expressions for the following :

Product of p and q added to 7

Question 8 :

Write the algebraic expressions for the following :

x more than two-third of y

Question 9 :

Write the algebraic expressions for the following :

Half a number x decreased by 3

Question 10 :

Write the algebraic expressions for the following :

Sum of numbers m and n decreased by their product

Question 11 :

Write the algebraic expressions for the following :

4 times x less than sum of y and 6

Question 12 :

Write the algebraic expressions for the following :

Double the sum of one third of a and m

Detailed Answer Key

Question 1 :

Write the algebraic expressions for the following :

Sum of x and twice y

Solution :

Twice y  =  multiply 'y' be 2 -----> 2y

Sum of x and twice y : 

x + 2y

Question 2 :

Write the algebraic expressions for the following :

Subtraction of z from y

Solution :

Subtraction of z from y : 

y - z

Question 3 :

Write the algebraic expressions for the following :

Twice the sum of m and n

Solution :

Sum of m and n  =  m + n

Twice  =  multiply by 2

Twice the sum of m and n :

2(m + n)

Question 4 :

Write the algebraic expressions for the following :

b is  decreased by twice a

Solution :

Twice a  =  multiply 'a' by 2 -----> 2a

b is decreased by twice a : 

b - 2a

Question 5 :

Write the algebraic expressions for the following :

Sum of x squared and y squared

Solution :

Square of x  =  x2

Square of y  =  y2

Sum of x squared and y squared :

x2 + y2

Question 6 :

Write the algebraic expressions for the following :

Two times the product of a and b divided by 5

Solution :

Two times the product of a and b  =  2ab

Two times the product of a and b divided by 5 : 

2ab / 5

Question 7 :

Write the algebraic expressions for the following :

Product of p and q added to 7

Solution :

Product of p and q  =  pq

Product of p and q added to 7 :

pq + 7

Question 8 :

Write the algebraic expressions for the following :

x more than two-thirds of y

Solution :

Two-thirds of y  =  (2/3)y

x more than two-thirds of y :

x + (2/3)y

Question 9 :

Write the algebraic expressions for the following :

Half a number x decreased by 3

Solution :

Half a number x  =  (1/2) x

Decreased by 3  =  - 3

Half a number x decreased by 3 :

(x/2) - 3

Question 10 :

Write the algebraic expressions for the following :

Sum of numbers m and n decreased by their product

Solution :

Sum of numbers m and n  =  m + n

Decreased by their product  =  -mn 

Sum of numbers m and n decreased by their product :

(m + n) - mn

Question 11 :

Write the algebraic expressions for the following :

4 times x less than sum of y and 6

Solution :

4 times x  =  4x

Sum of y and 6  =  y + 6

4 times x less than sum of y and 6 :

4x - (y + 6)

Question 12 :

Write the algebraic expressions for the following :

Double the sum of one third of a and m.

Solution :

One third of a and m  =  (1/3)a + m

Double =  multiply by 2

Double the sum of one third of a and m :

2[(1/3)a + m]

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