Word Problems

A word problem requires you to find an answer from the facts of the problem.

Here are some steps to follow:

Understand the problem. (Read and re-read it!)
- Do you understand all the words used in stating the problem?
- What are you asked to find?
- Can you restate the problem in your own words?
Devise a plan. Pick an approach and give it a try. For example:
- Guess and check.
- Look for a pattern.
- Draw a picture.
- Use a chart.
- Set up variables and solve an equation.
Carry out the plan.
Check your answer against the words of the problem to be sure that it makes sense.

Below are a few words and phrases to look out for when translating from English to mathematical symbols.

ENGLISH	MATH SYMBOLS
$3$ more than a number $3$ greater than a number $3$ units longer than/ older than/ taller than/ heavier than a quantity	$3 + x$
5 less than a number 5 units shorter than/ younger than/ lighter than/ nearer than a quantity	$x - 5$
$7$ diminished by a number / decreased by a number	$7 - x$
twice a number	$2 \cdot x$
$6$ times as many as a number $6$ times as long as/ as old as/ as tall as/ as heavy as a quantity	$6 \cdot x$
half as much as a number	$\frac{1}{2} x$
two thirds as much as a number	$\frac{2}{3} x$
the quotient of a number and $8$ a number divided by $8$	$\frac{n}{8}$
the square of a number	$x^{2}$
the cube of a number	$x^{3}$
is/is equal to/is the same as	=
is less than	<
is greater than/is more than	>
is at most / is no more than	$\leq$
is at least / is no less than	$\geq$

Also, the following four definitions are important:

Sum	Answer to an addition problem
Difference	Answer to a subtraction problem
Product	Answer to a multiplication problem
Quotient	Answer to a division problem

Example 1:

Five times a number $x$ is less than the sum of 3 and a number y .

"5 times a number $x$ " indicates multiplication: 5 x .

"is less than" indicates the < relation.

"the sum of $3$ and a number y " indicates addition: $3 + y$

Putting it all together:

$5 x < 3 + y$

Example 2:

Ten more than the quotient of a number $x$ and $30$ is equal to $15$ .

"Ten more than" indicates addition: $10 +$ .

"the quotient of a number $x$ and 30" indicates division: $\frac{x}{30}$

"is equal to 15" indicates the = relation: = $15$

Putting it all together:

$10 + \frac{x}{30} = 15$