Word problems can be some of the most difficult types of questions on any test. They will test your problem solving abilities, as you must figure out what the question is asking. When you first attempt a word problem, write all numbers and quantities to the side of the word problem, since it will be easier to manage the information when it is not surrounded by text. Also, see if there is any unnecessary information that you can eliminate from the problem. You can then begin solving the problem.

**Words That Mean Addition:**

- increased by
- added to
- more than
- combined
- together
- total of
- sum
- older than
- farther than
- greater than
- in all

*For 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

*For 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

*For 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

*For 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

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

Once you have read the word problem and translated key words to their operations, you must quickly decide what information is important. Make sure to write out formulas, underline content, and visually organize the information in written form.

**Problem**

A clothing store sells a coat for $137. In the spring, the store reduces the the price by 25%. How much does the coat sell for?

**Solution**

- Since the price is being
__reduced__, and the problem asks how much the coat__sells for__, you know you need to find how much the reduced coat will cost. - Assessing the information: the coat is $137, and the price is reduced by 1/4
- 137 × .25 = 34.25
- $137 - $34.25 = $102.75

You may also see questions which give an equation and ask you to determine which description best matches it. For example:

**Problem**

Which story best fits the equation 60 ÷ 5 = 12 ?

A) You have 60 quarters. After you spend 5 of them, how many quarters do you have left?

B) You share your 60 quarters with 4 of your friends, giving yourself and each of them an equal number of quarters. How many quarters does each person have?

C) You have 60 quarters and your friend has 5 quarters. How many quarters do you two have combined?

D) You have 60 quarters, and you decide to trade 5 of your quarters to your friend for 5 dimes instead. How much money did you lose by trading?

**Solution**

- Think about what math operations you would use to solve each part.
- For A, you would use subtraction; for B, you would use division; for C, you would use addition; and for D, you would likely use subtraction and addition.
- Thus, B is most likely to be correct, since 60 quarters divided amongst 5 people equals 12. This matches the equation above.

**Answers to Practice Problems**

- C
- D
- C

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