Download section 1.8 words into symbols

ALGEBRA II. NOTES
SECTION 1.8 WORDS INTO SYMBOLS
Algebra has a language of its own.
KEY WORDS / PHRASES TO LOOK FOR:
1.) ADDITION – plus, sum of, increased by, more than
2.) SUBTRACTION – minus, difference, decreased by, less than
3.) MULTIPLICATION – product of, times, of
4.) DIVISION – divided by, quotient of
5.) EQUALS – is, is equal to, are, was, will be
- use this to help you write an equation to represent the given sentence in terms
of a variable.
A.) WORD PROBLEM – describes a situation in which certain numbers are related to
each other.
So how do we go about setting up a word problem so that we can solve it?
1.) READ THE PROBLEM CAREFULLY:
a.) Decide what the unknowns are.
- some of the #’s are given – knowns
- others are values that must be determined from given facts –
unknowns
b.) Decide what the facts are.
- write them down in list form or draw sketch
- order in which the facts of a problem are used doesn’t matter.
- Sometimes you are given extraneous information that you don’t use.
2.) CHOOSE A VARIABLE TO REPRESENT THE UNKNOWNS:
a.) Choose a variable for 1 of the unknowns.
- ask yourself “to which quantity are the others in the problem being
compared to ?”
- ask yourself “how are the #’s related?”
b.) Write an expression for the other unknown in terms of the chosen variable
based on the facts given.
3.) REREAD THE PROBLEM AND WRITE AN EQUATION:
a.) Use the other facts from the problem to write an equation.
Examples:
1.) 7 less than a number
2.) three times the sum of a number and 8
3.) Find the measure of the 3rd angle of a triangle if the 1st angle has a measure of x
and the measure of the 2nd angle is 15 less than half the measure of the 1st angle.
4.) A car leaves town traveling at 40 mph. Two hours later, a 2nd car leaves the same
town on the same road traveling at 60 mph. In how many hours will the 2nd car pass the
1st car?
5.) What is the sum of 3 consecutive even integers?
Note: Consecutive Integers
Integers: ..., 2, 1, 0,1, 2,...
Representation
x, x  1, x  2,...
Even Integers: ..., 4, 2, 0, 2, 4,...
x, x  2, x  4,... where x is even
Odd Integers: ..., 3, 1,1,3,...
x, x  2, x  4,... where x is odd
Oral Exercises: pgs.45-46 #6-20