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:
Addition

Subtraction

Multiplication

Division

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 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 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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WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits