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".