Word problems can be some of the most difficult types of questions on any test. You have to understand precisely what the question is asking you and what relevance the quantities have to one another. For Arithmetic Word Problems, you will not really have to worry about creating algebraic expressions in order to answer the questions.

When you first attempt a word problem, write all quantities to the side of the word problem. You can better manage the information when it is not surrounded by text. Also, see if there is any superfluous information that you can eliminate from the problem. You can then determine the required mathematical operations from two places—within the word problem’s information or in the desired result (the question portion of the word problem). Review this list of translations from word to mathematical operation:

• increased by
• more than
• combined
• together
• total of
• sum
• older than
• farther than
• greater than
• in all

Example

The coat cost the store \$55 and its price was increased by \$30 so that the store could make a profit.

### Words that Mean Subtraction

• decreased by
• less than
• difference
• minus
• fewer than
• reduced by
• are left

Example

In a store‐wide sale, all \$55 jackets are reduced by 35% and \$30 shoes are reduced by 45%.

### Words that Mean Multiplication

• times
• product of
• multiplied by
• increased by a factor of
• twice
• decreased by a factor of

Example

The store sold 20 jackets in a sale at \$35 each. The store sold 30 hats at twice their original price of \$10.

### Words that Mean Division

• quotient
• divided equally among
• per
• half
• ratio of
• percent
• out of

Example

The school divided equally among its students 350 bags of candy.

### Words that Mean Equals

• is
• sells for
• given
• result
• are
• were
• will be
• equals
• gives
• yields
• sold for
• ultimately ends in

Example

What does each jacket sell for when the store has a 33% discount on winter-wear?