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Int. Alg. Notes
Section R.5
Page 1 of 3
Section R.5: Algebraic Expressions
Big Idea: An algebraic expression is a way of stating a multi-step arithmetic calculation where you want to
capture the steps of the calculation without necessarily using specific numbers, so you use letters (or variables)
to stand in for the specific numbers that may change depending on the situation.
Big Skill: You should be able to translate a multi-step calculation into an algebraic expression, evaluate
algebraic expressions given a specific number for the variable, simplify algebraic expressions by combining like
terms, and determine the domain of a variable in a given algebraic expression.
An algebraic expression is an expression consisting of constants, variables, grouping symbols, and symbols of
operations (addition, subtraction, multiplication, division, or exponents) arranged according to the order of
operations. Algebraic expressions are meant to capture the steps of a multi-step calculation without being
restricted to fixed numbers all the time.
Practice:
1. Translate the calculation for the total price of a purchase after 5.5% sales tax into an algebraic
expression.
2. Translate the calculation for the total price of numShirts shirts purchased at a cost of $29.99 each and
numPants pairs of pants purchased at a cost of $34.99 each into an algebraic expression.
3. If you made between $29,700 and $79,150 in 2007, then the income tax you owe (as a single filer) is
10% on the first $7,300, 15% on the amount between $7,300 and $29,700, and 25% on the remainder
above $29,700. Translate the calculation for 2007’s federal income tax into an algebraic expression.
4. Translate the English phrase twice the sum of a number x and 5 into an algebraic expression.
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.
Int. Alg. Notes
Section R.5
Page 2 of 3
Evaluating an Algebraic Expression: plug the given number in for the variable, then use the order of
operations to calculate a value.
Practice:
1. Evaluate the algebraic expression 5z  3 for z = 2.
2. Evaluate the algebraic expression
4n  n 2
for n = -5.
n2
3. Evaluate the algebraic expression 3 y  5 for y = 2/3.
Simplifying Algebraic Expressions by Combining Like Terms:
 A term is a number or the product of a number and one or more variables raised to a power.
Terms are combined using addition or subtraction.
 The number that multiplies the variables in a term is called the coefficient.
 Like terms have the same variable or variables, each raised to the same exponent.
 We can combine like terms into a single term by adding (or subtracting) the coefficients.
Practice:
1. Simplify the algebraic expression 2n  7n by combining like terms.
2. Simplify the algebraic expression r  7  5r by combining like terms.
3. Simplify the algebraic expression 8 y 2  3  2 y 2  11by combining like terms.
4. Simplify the algebraic expression 5k  6  3k 2  2k  3  9k 2  15b by combining like terms.
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.
Int. Alg. Notes
Section R.5
Page 3 of 3
Simplifying Algebraic Expressions by Removing Parentheses Using the Distributive Property:
Oftentimes, once parentheses are removed using the distributive property, there are like terms that can be
combined.
Practice:
1. Simplify the algebraic expression 2  3m  4  8m  2  .
2. Simplify the algebraic expression
2
2x 1
.
 6x  4 
3
6
Determining the Domain of a variable:
The set of values that a variable may assume is called the domain of the variable.
To determine the domain of a variable:
1. The context of the problem can give clues.
2. The nature of the calculation can give clues (namely, you can’t divide by zero).
Practice:
1. Determine the domain of 2x  7 .
2. Determine the domain of
4
.
x 5
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.