Download LESSON 1-3 NOTES: ALGEBRAIC EXPRESSIONS You can model

LESSON 1-3 NOTES:
ALGEBRAIC EXPRESSIONS
You can model words with algebraic expressions. In a word problem, look for words and word
phrases that indicate mathematical operations. List possible words and word phrases that indicate
each mathematical operation.
ADDITION
SUBTRACTION
MULTIPLICATION
DIVISION
EXAMPLES/PRACTICE: Write an algebraic expression that models the given word phrase.
1) seven fewer than a number n
2) two times the sum of a and b
3) nine less than 5 multiplied by the number p
4) quotient of 4 more than the number z
and the number y decreased by 3
EXAMPLE: Modeling a situation - You start with $20 and save $6 each week. What
algebraic expression models the total amount you save?
Define the variable. Let w = number of weeks.
Write as an algebraic expression:
PRACTICE: Modeling a situation - You had $150, but you are spending $2 each day. What
algebraic expression models this situation? Let d = number of days. [Hint: What
mathematical operation represents spending money in this situation?]
EVALUATE AN ALGEBRAIC EXPRESSION - To evaluate an algebraic expression, substitute
a number for each variable in the expression. Then simplify using the order of operations.
EXAMPLES/PRACTICE: Evaluate each algebraic expression for the given values of the variable.
5) 7(a + 4) + 3b - 8 for a = −4 and b = 5
7)
for x = 6 and y = −3
6)
+ y2 for x = 1 and y =
EXAMPLE: Writing and Evaluating an Expression - In football, a touchdown (TD) is worth
6 points, an extra-point kick (EPK) is 1 point, and a field goal (FG) is 3 points.
(A) Define each variable.
(B) Write an algebraic expression that models the total number of points that a football team
scores in a game, assuming each scoring play is one of the three given types.
(C) Suppose a football team scores 3 touchdowns, 2 extra-point kicks, and 4 field goals. How
many points did the team score?
PRACTICE: Complete "Got It? Problem 4" on page 20 of your textbook.
An expression (numerical or algebraic) consists of terms. A term is a number, a variable, or the
product of a number and one or more variables. A coefficient is the numerical factor of a term. A
constant term is a term with no variables.
Examples:
3x − 5y
-4ax + 7w − 6
two terms, coefficients are 3 and -5
three terms, coefficients are -4 and 7, constant term is -6
Like terms have the same variables raised to the same powers.
Examples: 3x2 + 5x2 + 9y3z + 2yz − 4y3z
Like Terms: 3x2 and 5x2; 9y3z and −4y3z
You can simplify an algebraic expression that has like terms. You combine like terms using the
properties of real numbers. An expression and its simplified form are equivalent. Their values are
equal for all values of their variables.
EXAMPLES/PRACTICE: Simplify each algebraic expression by combining like terms.
8) 7x2 + 3y2 + 2y2 − 4x2
9) −(3k + m) + 2(k − 4m)
10) −4j2 − 7k + 5j + j2
11) −(8a + 3b) + 10(2a − 5b)