"Communication is fraught with peril; FRAUGHT, I say, with peril!"

David E. Brown

# Brother Brown's Mathematics Reference Pages:

# Translating English into math

When you’re translating from English into math, certain key words help you know what arithmetic operation you need. This page is a reference guide, offereing examples of these key words. If you find others, you can add them to these lists.

## Addition:

sum, plus, total, increased by, in addition, additionally, added to, mix, combine, more than (as in, “six more than the height”)

## Subtraction:

difference, minus, decreased by, subtracted from, what remains, take away, take from, separate, cut into parts of not necessarily equal size, less than (as in “six less than the height”), less (as in “revenue less commissions paid”)

## Multiplication:

product, of (**but not "out of"**), times, twice (which means " times 2"), double (which also means "times 2"), thrice or triple (both of which mean "times 3"), multiplied by, percent of (Of course, if it’s “percent of” then after multiplying you will use the % sign and either divide by 100 or move the decimal two places left.)

## Division:

quotient, ratio, per, go into, out of (**but not "of" by itself**), divide, half of, third of, etc., cut into equal parts, percent (which means “divide by 100")

## Equality:

is, are, equals, equal to, same, same as, result in, resulting in, yields, yielding

## Inequality:

### ≥

at least, no less than, not less than, greater than or equal to

### ≤

at most, no more than, not more than, less than or equal to

### >

greater than, more ... than (as in, “...is more expensive than...”), above, higher than, later than

### <

less than, less ... than (as in, “...is less expensive than...”), below, lower than, sooner than, not as much as

Sometimes a key word for inequality isn’t staring you in the face. Sometimes you have to infer its presence, as in “Which of the two is the better deal?” As soon as you see “better,” you know that inequality is involved, but which kind of inequality will depend on what “better deal” means and on the nature of the information given in the problem.

You sometimes see things like “the lesser of” or “the greater of;” these also refer to inequality, but translating them into math is a bit more complex than writing a ‘<’ or a ‘>’. If you want to know more about this, come ask me or talk to someone who knows waht they're doing.

## Comments:

When key words are not explicitly stated in the word problem, they can often be inferred from the context. Let experience be your guide, and **make sure you have read, internalized, and understood every word, every syllable, every punctuation mark, and every symbol in the statement you're trying to translate. Grammar can also be very important in translating. ** Meanwhile, if you ever have trouble translating English into math, come talk to me, or to anyone who has this figured out.