Suppose you know the area of a circle is approximately
is the radius of the circle. What if a circle has a radius of 25 inches? How would you find its area? In this Concept, you'll learn how to substitute 25 inches into the expression representing the area and evaluate the expression.
Just like in the English language, mathematics uses several words to describe one thing. For example,
sum, addition, more than,
all mean to add numbers together. The following definition shows an example of this.
means to follow the verbs in the math sentence.
can also be called simplify or answer.
To begin to evaluate a mathematical
, you must first
a number for the variable.
means to replace the variable in the sentence with a value.
Now try out your new vocabulary.
Evaluate means to follow the directions, which is to take 7 times
and subtract 11. Because
is the number 4, we can evaluate our expression as follows:
7×4−1128−1117The solution is 17.We have “substituted” the number 4 for y.We have multiplied 7 and 4.We have subtracted 11 from 28.
Because algebra uses variables to represent the unknown quantities, the multiplication symbol
is often confused with the variable
. To help avoid confusion, mathematicians replace the multiplication symbol with parentheses ( ) or the multiplication dot
, or by writing the expressions side by side.
with alternative multiplication symbols.
can be written as
It can also be written as
The following is a real-life example that shows the importance of evaluating a mathematical variable.
To prevent major accidents or injuries, these horses must be fenced in a rectangular pasture. If the dimensions of the pasture are 300 feet by 225 feet, how much fencing should the ranch hand purchase to enclose the pasture?
Begin by drawing a diagram of the pasture and labeling what you know.
To find the amount of fencing needed, you must add all the sides together:
By substituting the dimensions of the pasture for the variables
, the expression becomes:
Now we must evaluate by adding the values together. The ranch hand must purchase
feet of fencing.
1. Write the expression
in a more condensed form and then evaluate it for
2. If it costs $9.25 for a movie ticket, how much does it cost for 4 people to see a movie?
can be written as
. We can substitute 3 for
2. Since each movie ticket is $9.25, we multiply this price by the 4 people buying tickets to get the total cost:
It costs $37 for 4 people to see a movie.
Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both.
CK-12 Basic Algebra: Variable Expressions
In 1 – 4, write the expression in a more condensed form by leaving out the multiplication symbol.
In 5 – 9, evaluate the expression.
In 10 – 17, evaluate the expression. Let
a=−3, b=2, c=5,
In 18 – 25, evaluate the expression. Let
x=−1, y=2, z=−3,
In 26 – 30, evaluate the expression in each real-life problem.
The measurement around the widest part of these holiday bulbs is called their
The formula for circumference is
is the radius of the circle. Suppose the radius is 1.25 inches. Find the
Christmas Baubles by Petr Kratochvil
The dimensions of a piece of notebook paper are 8.5 inches by 11 inches. Evaluate the writing area of the paper. The formula for area is length
Sonya purchased 16 cans of soda at $0.99 each. What is the amount Sonya spent on soda?
Mia works at a job earning $4.75 per hour. How many hours should she work to earn $124.00?
The area of a square is the side length squared. Evaluate the area of a square with a side length of 10.5 miles.