The practice quiz for this study guide can be found at:

Mathematics for Nursing School Entrance Exam Practice Problems

Many of the math problems on tests are word problems. A word problem can include any kind of math, including simple arithmetic, fractions, decimals, percentages, and even algebra and geometry.

The hardest part of any word problem is translating 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 only hints at the mathematical operation to be performed. Here are the translation rules:

**EQUALS keywords: is, are, has**

EnglishMathBob is18 years old.b= 18There are7 hats.h= 7Judi has5 cats.c= 5

**ADDITION keywords: sum, more than, greater than, older than, total, altogether**

EnglishMathThe sumof two numbers is 10.x+y= 10Karen has $5 more thanSam.k= 5 +sThe base is 3 inches greater thanthe height.b= 3 +hJudi is 2 years older thanTony.j= 2 +tThe totalof three numbers is 25.a+b+c= 25How much do Joan and Tom have altogether?j+t= ?

**SUBTRACTION keywords: difference, fewer than, less than, younger than, remain, left over**

EnglishMathThe differencebetween two numbers is 17.x–y= 17Mike has 5 fewercatsthantwice the number Jan has.m= 2j– 5Jay is 2 years younger thanBrett.j=b– 2After Carol ate 3 apples, rapplesremained.r=a– 3

**MULTIPLICATION keywords: of, product, times, each, at**

EnglishMath20% ofthe samples0.20 × sHalf ofthe bacteria× bThe productof two numbers is 12.a×b= 12

**DIVISION keyword: per**

EnglishMath15 drops perteaspoon22 miles pergallon

### DISTANCE FORMULA: DISTANCE = RATE × TIME

You know you will need to use the distance formula when you see movement words like: plane, train, boat, car, walk, run, climb, or swim.

- How far did the
**plane**travel in 4 hours if it averaged 300 miles per hour? - Ben
**walked**20 miles in 4 hours. What was his average speed?

*D* = 300 × 4

*D* = 1,200 miles

20 = *r* × 4

5 miles per hour = *r*

### Solving a Word Problem Using the Translation Table

Remember the problem at the beginning of this chapter about the jelly beans?

Juan ate of the jelly beans.Maria then ate of the remaining jelly beans, which left 10 jelly beans. How many jelly beans were there to begin with?

- 60
- 80
- 90
- 120

We solved it by working backward. Now let's solve it using our translation rules.

Assume Juan started with *J* jelly beans. If Juan ate of them, that means there were of them left, or × *J* jelly beans. Maria ate a fraction of the **remaining** jelly beans, which means we must **subtract** to find out how many are left. Maria ate , leaving **of** the × *J* jelly beans, or × × *J* jelly beans. Multiplying out × × *J* gives *J* as the number of jelly beans left. The problem states that there were 10 jelly beans left, meaning that weset × *J* **equal **to 10:

× *J* = 10

Solving this equation for *J* gives ** J = 60**. Thus, the right answer is choice

**a**(the same answer we got when we

*worked backward*). As you can see, both methods—working backward and translating from English to math—work. You should use whichever method is more comfortable for you.

The practice quiz for this study guide can be found at:

Mathematics for Nursing School Entrance Exam Practice Problems

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