In these lessons, we will learn how to write algebraic expressions for word problems. We will start with some common phrases found in word problems.
Related Topics:
More Algebra Word Problems
More Algebra Topics
Phrase to Algebraic Expression
To write an expression, we often have to interpret a written phrase.
For example, the phrase “ 6 added to some number” can be written as the expression x + 6, where the variable x represents the unknown number.
Some examples of common phrases and corresponding expressions that involve addition are:
Phrase 
Expression 
4 more than some number 
x + 4 
a number increased by 10 
y + 10 
8 plus some number 
t + 8 
the sum of a number and 12 
w + 12 
Some examples of common phrases and corresponding expressions that involve
subtraction are:
Phrase 
Expression 
4 less than some number 
x – 4 
a number decreased by 10 
y – 10 
8 minus some number 
8 – t 
the difference between a number and 12 
w – 12 
Some examples of common phrases and corresponding expressions that involve
multiplication are:
Phrase 
Expression 
4 times some number 
4x 
twice a number 
2y 
onethird of some number 

the product of a number and 12 
12w 
Some examples of common phrases and corresponding expressions that involve
division are:
Phrase 
Expression 
the quotient of 4 and some number 

a number divided by 2 

the ratio of 8 and some number 

the quotient of a number and 12 

Some examples of common phrases and corresponding expressions that involve
two operations are:
Phrase 
Expression 
6 more than 5 times a number 
5x + 6 
4 times the sum of a number and 7 
4(y + 7) 
5 less than the product of 3 and a number 
3w – 5 
twice the difference between a number and 9 
2(z – 9) 
How Do You Write Mathematical Expressions from Word Problems?
There are so many words that you come across when you're working on algebra problems, and these words are really code for very specific mathematical symbols.
How to write algebraic expressions for word phrases, by analyzing the language used?
An algebraic expression is a mathematical phrase that contains a combination of numbers, variables and operational symbols.
A variable is a letter that can represent one or more numbers.
How to write expressions with variables?
Examples:
Write the algebraic expressions to represent the statements.
a) The sum of 7 and the quantity 8 times x
b) Take the quantity 3 times x and then add 1.
c) 6 plus the product of 1 and x.
How to write algebraic expressions with parentheses?
Examples:
1: First consider the expression for
5 plus the quantity of 4 times x
Now take the product of 8 and that expression and then add 6.
2: First consider the expression for
the sum of 7 and the product of 2 and x
What expression would be:
4 plus the quantity of 2 times that expression
How to Write Algebraic Expressions for Situations?
Example:
Translate the following phrases into algebraic or numeric expressions.
a) 173 less than a number 'b'
b) Quotient of 173 and 'b'
c) 'b' times 173
d) 173 more than 'b'
How to Write Equations from Word Problems?
This video teaches how to dissect a word problem in order to define a variable and write an equation.
Example:
1: Half of a number is 16. Write an equation to represent the situation. Define your variable and solve.
2: Mrs. Gaddie has two dogs. Her friend AnnaMarie has three less than twice as many as Mtr. Gaddie. How many dogs does AnnaMarie have?
3: A recycling plant recycles 2 tons of cans yesterday. This is a third of their usual amount. How much does the plant usually recycle?
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