Variable Expressions consists of numbers, operations and symbols or letters to represent unknown values. In the lesson
Introduction to Variables, we found that we can define the perimeter of a square using variables as:
4(s)
where s is the length of one side of the square.
4(s) is an example of a variable expression. With variable expressions, we can substitute numbers for the variables and solve the expression.
Examples
- Evaluate 4 + n when n = 5.
With this expression we are given that n = 5. We substitute 5 in place of the n to get:
4 + n = 4 + 5 = 9
- Evaluate y/4 when y = 8.
First we substitute 8 for y.
y/4 = 8/4
Then we divide
8/4 = 2
- Evaluate 5 + y + z when y = 4 and z = 6.
First substitute 4 for y and 6 for z.
5 + y + z = 5 + 4 + 6
Then solve:
5 + 4 + 6 = 15
Notes About Multiplication in Expressions
When dealing with multiplication in expressions you must resist the urge to use the × sign as it can often be confused with the variable x. Instead write multiplication expressions in the following ways:
4s
4(s)
4*s - This is useful for computes, however when using pencil and paper, it's not necessary to use this form.
You must also make sure that when substituting values for variables, you use the second form presented above. Lets look at an example:
Find the perimeter of a square who's sides each have a length of 2.
If we are finding the perimeter of a square we know that we can use the expression 4s where s is the length of a side. We need to be careful of how we do the substitution however. If we substitute the 2 in for s exactly as it's written we get:
4s = 42
which is not the correct answer. Instead we must use the second form:
4s = 4(s) = 4(2) = 8
This method gives us the correct answer and clearly indicates we must multiply the 4 times the 2 to get our answer.