# WRITING VARIABLE EXPRESSIONS

## About "Writing variable expressions"

Writing variable expressions :

Writing variable expressions is the most important topic in math. Whenever we want to solve word problems, first we have to understand the given statement and convert the words into algebraic expression.

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

• The sum of
• increased by
• plus
• added to
• more than

## Subtraction

• the difference of
• decreased by
• minus
• subtracted from
• less than

## Multiplication

• the product of
• multiplied by
• times

## Division

• the quotient of
• divided by
• the ratio of

## Writing variable expression - Examples

Let us see some examples based on the above concept.

Example 1 :

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)

Example 2 :

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 3 :

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 4 :

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 5 :

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 6 :

Write the algebraic expressions for the following:

x more than two-third of y

Solution :

Since we have the word "more than", we have to use the binary operator "+"

two-third of y  =  (2/3)y

x more than two-third of y  =  x + (2/3)y

Example 7 :

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 8 :

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 9 :

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 10 :

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]

After having gone through the stuff given above, we hope that the students would have understood "Writing variable expressions".

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