**Algebra Word Problems
– Real Life Applications**

Word problems are the biggest obstacle for students taking algebra. Every Student needs a plan of action to overcome the fear of the word problems in algebra. The starting point really beings with English. In other words the words need to be translated in mathematical terms. The information which includes numbers and unknowns must be identified. The key to translation is practice. It takes practice to decipher or uuencode a word problem. This process or strategy is essential in real life to code breaking or the finding the cure or solution to delete a “virus” on a computer.

It is this process of breaking the problem apart; this thought process that makes problem solving a valuable skill in real life.Math provides us the experience for solving problems. Whenever we make a decision about whether or not to choose a certain transportation choice for a vacation or stay at a certain hotel, mathematics is involved in the decision.

**Algebra Word Problems
– Types**

The main types of word problems involve area, perimeter, work, rate, distance, mixture, and a system of equations. A key component about understanding these problems is connected to properly translating the words into an algebra expression. The following operations are connected to certain words in algebra. A student should know the following terms:

Addition - increased by, more than, combined, together, total of sum, added to.

Subtraction - decreased by, minus, less, difference between/of less than, fewer than.

Multiplication –
of, times, multiplied by, product of, increased/decreased by a factor of (this
type can involve both addition or subtraction *and *multiplication!).

Division - per, a, out of, ratio of, quotient of percent (divide by 100).

Equals - is, are, was, were, will be, gives, yields, sold for.

**Algebra Word
Problems - Extra Notes**

Note that
"per" means "divided by", as in "I drove 80 miles on
three gallons of gas, so I got 20 miles per gallon". Also, "a"
sometimes means "divided by", as in "When I tanked up, I paid $11.97 for three gallons, so the gas was $3.99 a gallon".Warning: The "less
than" construction is backwards in the English from what it is in the
math. If you need to translate "4.5 less than *x*", the temptation is to write "4.5 –* x*".

*Do not do this!* You can see how this is wrong by
using this construction in a "real world" situation: Consider the
statement, "He makes $4.50 an hour less than me." You do not figure
his wage by subtracting your wage from $1.50. Instead, you subtract $4.50 from your wage.

So remember; **the "less than" construction is
backwards.**Also note that order is
important in the "quotient/ratio of" and "difference
between/of" constructions. If a problems says "the ratio of *x* and *y*", it means "*x* divided by *y*", not "*y* divided by *x*". If the problem says "the difference
of *x* and *y*", it means "*x* – *y*", not "*y* – *x*".

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