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1 Evaluating Expressions
What Are Monomials?
A monomial is a single algebraic expression involving no addition and no subtraction.
These are monomials: m, 2n, tw, and s2.
These are not monomials: w + s, 3m − n.
A monomial is called a term in an algebraic expression.
How Do You Add Monomials?
When you add, you put things together. This number line models 3m + 2n.
m
m
m
n
n
3m + 2n
0
So does this design.
=m
=n
If you add monomials with the same variables, you can show sums more simply.
For example, m + 2m can be rewritten as 3m.
That makes sense since one of something and two more of the same thing is 3 of
that thing.
m
0
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m
m
3m
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1 Evaluating Expressions (continued)
How Do You Subtract Monomials?
When you subtract, you might be figuring out one of the following:
• What is left if you remove something from something else
• How much more one amount is than another
• What you need to add to one amount to get to the other amount
For example, 3m − m = 2m can tell you that if you take 1 of something from 3 of the
same thing, there are 2 of that thing left.
m
m
m
2m
0
–m
3m − 2n can tell you how much more 3m is than 2n or what you must add to 2n to
get to 3m.
m
0
m
n
m
3m – 2n
n
If you subtract monomials that have the same variables, you can show differences
more simply.
For example, 5n − 2n = 3n.
n
n
n
n
n
How Do You Evaluate Algebraic Expressions?
You evaluate an algebraic expression by substituting assigned numbers for each
variable and performing normal number computations.
For example, if m = 2 and n = 3.1, the expression 3n − 2m has the value 9.3 − 4 = 5.3.
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Grade 7 • Algebra
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1 Evaluating Expressions (continued)
How Do You Evaluate Algebraic Expressions? (continued)
You use the same process to evaluate measurement formulas.
For example, you can determine the area of a rectangle using the formula l × w.
If l = 10 and w = 2, the area is 10 × 2 = 20 square units.
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10
How Do You Create an Expression With a Particular Value
When You Know the Values of the Variables?
If you know the values of the variables involved, you can create algebraic
expressions that have particular values.
For example, if you know m = 2.75 and n = 3.25 and you want an expression worth
9.25, you can create the expression 2n + m.
Definitions
algebraic expression: a combination of variables, numbers, and/or operation
symbols, for example, x + 7, 12n + 2, 3(a − b), n2
evaluate (an expression): to determine the value of an algebraic expression for a
certain value of the variable or variables
monomial: an algebraic expression involving no addition or subtraction,
for example, 3s, 4, or m × n
term (algebra): a monomial, for example, 3n, ah, or 12by
variable: a letter, shape, or other symbol such as w, p, or
that represents a
number; for example, in the equation 3 + a = 12, a is a variable
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Grade 7 • Algebra
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