Algebraic expression word problems examples with answers :
Here we are going to learn how to write algebraic expressions for word problems.
The following table will help us to learn some of the words (phrases) that can be used to indicate mathematical operations: Algebraic expression word problems examples with answers
Addition
Multiplication

Subtraction
Division

Example 1 :
Write the algebraic expressions for the following:
Sum of x and twice y
Solution :
Since we have the word "sum of", we have to use the binary operator "+"
Twice y = multiply "y" be 2 ==> 2y
Sum of x and twice y = x + 2y
Hence the algebraic expression for the given statement is x + 2y. Writing algebraic expressions from word problems worksheets
Example 2 :
Write the algebraic expressions for the following:
Subtraction of z from y.
Solution :
Since we have the word "Subtraction", we have to use the binary operator ""
Subtraction of z from y = y  z
Hence the algebraic expression for the given statement is y  z.
Example 3 :
Write the algebraic expressions for the following:
Twice the sum of m and n.
Solution :
Since we have the word "sum of m and n", we have to use the binary operator "+"
Sum of m and n = m + n
twice = multiply by 2
Twice the sum of m and n = 2(m + n)Writing variable expressions worksheet
Example 4 :
Write the algebraic expressions for the following:
b decreased by twice a
Solution :
Since we have the word "decreased by", we have to use the binary operator ""
twice a = multiply 2 by a
b decreased by twice a = b  2a
Example 5 :
Write the algebraic expressions for the following:
Numbers x and y both squared and added.
Solution :
Since we have the word "added", we have to use the binary operator "+"
square means we have to take power 2 for the variable
x and y both squared and added = x² + y²
Example 6 :
Write the algebraic expressions for the following:
Two times the product of a and b divided by 5
Solution :
Since we have the words "product of a and b", and "divided by", we have to use the binary operators "x" and "/".
Two times the product of a and b = 2ab
Two times the product of a and b divided by 5 = 2ab/5
Example 7 :
Write the algebraic expressions for the following:
Product of p and q added to 7.
Solution :
Since we have the words "product" and "added", we have to use the binary operators "x" and "+".
Product of p and q = pq
Product of p and q added to 7 = pq + 7
Example 8 :
Write the algebraic expressions for the following:
x more than twothird of y
Solution :
Since we have the word "more than", we have to use the binary operator "+"
twothird of y = (2/3)y
x more than twothird of y = x + (2/3)y
Example 9 :
Write the algebraic expressions for the following:
Half a number x decreased by 3.
Solution :
Since we have the word "decreased by", we have to use the binary operator ""
Half a number x = (1/2) x
decreased by 3 =  3
Half a number x decreased by 3 = (x/2)  3
Example 10 :
Write the algebraic expressions for the following:
Sum of numbers m and n decreased by their product
Solution :
Since we have the words "Sum of" and "decreased", we have to use the binary operator "+" and ""
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
Example 11 :
Write the algebraic expressions for the following:
4 times x less than sum of y and 6.
Solution :
Since we have the words "less than" and "sum of" , we have to use the binary operator "" and "+"
4 times x = 4x
sum of y and 6 = y + 6
4 times x less than sum of y and 6 = 4x  (y + 6)
Example 12 :
Write the algebraic expressions for the following:
Double the sum of one third of a and m.
Solution :
Since we have the word "sum of", we have to use the binary operator "+"
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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