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# Dealing with Word Problems Study Guide (page 2)

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Updated on Oct 4, 2011

## Translating Word Problems

The hardest part of any word problem is translating from English into math. When you read a problem, you can frequently translate it word for word from English statements into mathematical statements. At other times, however, a key word in the word problem hints at the mathematical operation to be performed. The translation rules follow this explanation.

#### Tip

When reading a word problem, cross out all the unnecessary words that do not directly pertain to the math. They only serve as a distraction, and your process will be more visible when they're removed.

### EQUALS                    Key words: is, are, has

 English Math Bob is 18 years old. B = 18 There are 7 hats. h = 7 Judi has 5 books. J = 5

### ADD                             Key words: sum; more, greater, or older than; total; altogether

 English Math The sum of two numbers is 10. x + y = 10 Karen has \$5 more than Sam. K = 5 + S The base is 3" greater than the height. b = 3 + h Judi is 2 years older than Tony. J = 2 + T Al threw the ball 8 feet further than Mark. A = 8 +M The total of three numbers is 25. a + b + c = 25 How much do Joan and Tom have altogether? J + T = ?

### SUBTRACT                Key words: difference; fewer, less, or younger than; remain; left over

 English Math The difference between two numbers is 17. x – y = 17 Jay is 2 years younger than Brett. J = B – 2 (NOT 2 – B) After Carol ate 3 apples, r apples remained. r = a – 3 Mike has 5 fewer cats than twice the number Jan has. M = 2J – 5

### MULTIPLY                   Key words: of, product, times, twice

 English Math 25% of Matthew's baseball caps 0.25 × m, or 0.25m Half of the boys The product of two numbers is 12. a × b = 12, or ab = 12 Murray has twice as many cards as Tina. M = 2T [Notice that it isn't necessary to write the times symbol (×) when multiplying by an unknown.

### DIVIDE                            Key word: per

 English Math 15 blips per 2 bloops 60 miles per hour 22 miles per gallon

#### Tip

Converting Decimals and Fractions into Time: Remember, decimals are based on units of 10, while seconds and minutes are based on units of 60, so be careful when converting information in word problems! When faced with time as a decimal or fraction, multiply the fraction or decimal portion by 60 to convert it into seconds.

Example: 7.6 minutes: 0.6 × 60 = 36 seconds, so 7.6 minutes = 7 minutes 36 seconds.
Example:hours: × 60 = 40 minutes, sohours = 4 hours 40 minutes.

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