This equation means that f, which is the variable representing our unknown number or value, is being multiplied by 5 to equal 23. Here’s what this looks like:
f x 5 = 23
Out loud, this can sound like:
“f times five equals twenty three”
or
“An unknown number times 5 will equal 23”
If you want to actually solve for the answer, follow along with these steps below:
*** As a reminder, our original equation is ***
f (5) = 23.
••• STEP ONE: •••
Since we know that f is being multiplied by 5, we can remove the parenthesis and rewrite the equation.
f (5) = 23
Rewritten as:
f x 5 = 23
••• STEP TWO: •••
We now have f x 5 = 23. We need to isolate our variable on one side of the equation. To put it differently, we need to get the letter f ( our variable) to be by itself on one side of the = sign. Since f is currently being multiplied by 5, all we need to do is the opposite of multiplication to counteract this, which is division. Therefore, we can divide both sides of the equation by the number 5 so as to isolate our variable. Here’s what it looks like to divide our equation by 5, where the denominator represents the division:
f x 5 23
____ = ___
5 5
^Note that on the left hand side of the equation, we are diving f x 5 by 5 (f x 5 / 5). Again, we are isolating our variable in this step. So, the two 5s on the left side cancel each other out because we are using opposite processes (multiplication to division) with the same equal number to eliminate the “times 5” on the left side and be left with only the remaining f. Being said, we have isolated our variable and we no longer need to worry about the 5 on the left side of the equation, as it has been cancelled out. We are now simply left with our variable f on the left hand side.
Now that our variable is isolated, we are left with f on the left side of the = sign, and 23 divided by 5 on the right hand side. The problem looks like this:
23
f = ___ or f = 23 ÷ 5
5
The equations above are equal, and they both show that our variable (f) is equal to 23/5.
••• STEP THREE: •••
Since we now know that f = 23 divided by 5, we can use a calculator or long division to divide 23 by 5. When we do this, we get the decimal 4.6.
**Please note that there are many different ways to write this answer. Above, I have just shown you this fraction (23/5) as a decimal (4.6). If you are solving this equation for an assignment, check what form your instructor wants you to use as the final answer.**
If you were looking for a decimal, you are done with this equation, as we have found the decimal 4.6.
Below, I will include some alternative ways you may write a solution of this equation as a final answer.
Initial equation: f (5) = 23
• FINAL ANSWER:
- Final answer as a decimal:
f = 4.6
- Final answer as a fraction
(in simplest form):
23
f =. ___ or f = 23/5
5
- Final answer as a mixed number:
3
f = 4 ___ or f = 4 3/5
5
(“f equals four and three fifths”)
- Final answer as a percentage:
f = 460%
I really hope this helps!