OML Search

Writing Expressions




 

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

one-third 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.


 
Write word problems as algebraic expressions
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.
Writing Expressions 1
Write the algebraic expressions to represent the statements.
The sum of -7 and the quantity 8 times x
Take the quantity -3 times x and then add 1.
-6 plus the product of -1 and x.


Writing Expressions 2
How to write algebraic expressions with parentheses?
Example 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.

Example 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
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'


 
Writing 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.
Example 2: Mrs. Gaddie has two dogs. Her friend Anna-Marie has three less than twice as many as Mtr. Gaddie. How many dogs does Anna-Marie have?
Example 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?


You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.


OML Search


We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.


[?] Subscribe To This Site

XML RSS
follow us in feedly
Add to My Yahoo!
Add to My MSN
Subscribe with Bloglines