With all the formulas out there, how do you know which one to pick? And how do you read formulas anyways? Watch this video lesson and you will find the answers to these questions.
Why Do We Need Math Formulas?
Why do we need to know about formulas in math? Couldn't we just get by with our basics like adding, subtracting, multiplying, and dividing? Sure, but it would take us that much longer to solve a problem. Math formulas, which are equations that show us how to work something out, tell us exactly what we need to do to solve a particular problem. If we didn't use formulas, then we would have to do all the work that led up to the formula ourselves to find our answer. For example, if we wanted to find the volume of a box, we could either use the formula for the volume of a box, V = l * w * h, or we could use our basics and spend quite a bit of time to figure out that to find the volume of a box, we need to multiply its length, width, and height. Either way we go about it, the formula finds its way in. We can either use it to help us, or we can do things the hard way. I think letting formulas help us is the way to go.
Reading a Formula
So, if we are going to use formulas, how do we read them?
Let's look at an example.
Say we want to solve a quadratic equation, which is an equation whose highest exponent is 2, such as x^2 + 3x + 2 = 0. For these types of equations, we can use the quadratic formula. The formula tells us how to solve quadratic equations. It looks like this.
At first, this just looks like a bunch of letters with not much meaning. But this formula also tells us for what kinds of equations it will work. It works for equations in the form of ax^2 + bx + c = 0. Ah, we have more letters now. But this equation looks somewhat like ours. I see an x^2, an x, and a 0. The only things different here are the numbers where the letters are. What does that tell me? Why, it tells me what those letters are equal to for my problem equation. I have my a = 1, my b = 3, and my c = 2. Oh wait, would you look at that! Those are the letters in my formula. So, I can plug my numbers into the formula to find my answer. Now, I have this.
Input the letter equivalents to use the quadratic formula to solve
Would you look at that! My formula has turned into something I can evaluate. The plus/minus symbol tells me that I will be splitting this formula up into two parts. Before I do that, though, I go ahead and evaluate as much as I can. So I multiply the 4 with the 1 and 2 to get 8. I square the 3 to get 9. I subtract the 8 from the 9 to get 1 under the square root. I multiply the 2 and the 1 in the denominator to get 2.
I'm looking even better now. What is the square root of 1? It's 1. So now, I can split my equation into two parts, one plus part and one minus part. I get x = (-3 + 1)/2 and x = (-3 - 1)/2. Evaluating both of these separately, I get x = -1 and x = -2. I got my answers!
If I didn't have the use of this formula, solving my quadratic would be that much harder and would take even more time! As we saw, reading a formula is about matching our letters to the appropriate parts of our problem and then plugging those values back into the formula. Once we have matched all our letters and plugged them in, it's just a matter of evaluating.
How to Choose a Formula
Yes, formulas really do make our lives easier. But, how do you choose which formula to use? We do this by carefully reading our problem to find out what they are looking for. Once we know what they are looking for, then we look for the formula that deals with that question.
For example, say we have this problem:
Joe needs to know how much fencing he needs to buy so that he can fence up his rectangular yard. His yard measures 10 feet wide by 12 feet long. How much fencing does he need?
What do we need to help Joe out? It sounds like Joe needs to know the perimeter of his yard. Do we have a formula for the perimeter of a rectangle? Why, yes we do. It is the formula P = 2 * l + 2 * w. The l stands for length and the w stands for width. And, of course, the P stands for perimeter.
How do we use this? We do the same thing we did with our quadratic formula. We match our letters to our values from the problem and then we plug them in. I have my length as 12 and my width as 10. I plug these into my formula to get P = 2 * 12 + 2 * 10. Now, I go ahead and evaluate to get P = 24 + 20 which equals P = 44 feet. So, Joe needs 44 feet of fencing.
Do you see how our formula has helped us and Joe find the answer quickly and without too much pain?
Let's look at one last example.
Mary wants to install carpet in her living room. She needs to know how much carpet to buy. Her living room measures 7 feet by 12 feet. How much carpet does she need to cover the whole space?
What does this problem want us to find? It wants us to find the area of Mary's living room since the area tells us how much floor space is inside those measurements. Do we have a formula to help us? We sure do. We have the formula for the area of a rectangle, which is A = l * w where l is the length and w the width. I know what both l and w equal so I can go ahead and plug those values into the formula to get A = 12 * 7. Now I can evaluate to get my area of 84 square feet. So, Mary needs 84 square feet of carpet.
We are nearing the end of our video lesson, so let's review what we've learned. We've learned that math formulas are equations that show us how to work something out. We use them to help us solve problems easier and faster. The way we use them is to first read our problem carefully to find out what it's asking for and then look for a formula that gives us the answer to our problem. Once we have our formula, we match the letters in the formula to the values from the problem and we plug in those values. Once we have plugged in all our necessary values, we go ahead and evaluate our formula to find our answer.
After reviewing this video lesson, you could understand how to:
- Understand the importance of math formulas
- Display your ability to read and select a formula
- Plug in the required values and solve the equation