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At a Glance - Formulas

Here's video to help illustrate a few formulas.

It's been a loooong time since you've needed to deal with formula on a daily basis. You probably transitioned to solid foods at around five months, but now, it's back. 

Actually, that formula is gone forever, but mathematical formulas are here to stay forever. Everyone knows that mathematical formulas are twice as delicious, anyway.

In math a formula, like an equation, is a group of symbols that forms a meaningful mathematical statement. However, we call some equations "formulas" because they help us solve a type of math problem, not just a single math problem.

The equation A = lw is the formula for the area of a rectangle because it helps us find the area of any and all rectangles, not just one.

Sample Problem

Draw a rectangle with side lengths l and w. On second thought, save yourself the trouble—we'll draw one for you. We're really good at rectangles.

Rectangle with width w and length l.

Let A represent the area of the rectangle. Then, the equation A = lw is a formula describing A in terms of l and w.

Sample Problem

What does the formula for the circumference of a circle C = 2πr tell us to do? 

The formula says that to find the circumference C, we've gotta multiply the radius r by 2π. The equation is a formula because we can find the circumference of any circle using it.

Sample Problem

Stacy came up with the equation 2n + 3y = -1/2 to find the area of a square, and it worked. The formula gave Stacy the correct area of the square, but it didn't work for the next square. Is 2n + 3y = -1/2 a formula for the area of a square?

Not this time. For an equation to be a formula, it must help find the solution for an entire type of math problem. Stacy created the equation to find the answer of a single problem, so this equation hasn't reached formula status yet.

Sample Problem

Is the Pythagorean theorem a formula?

No...well...kinda...actually, no. No, it's not. But the Pythagorean theorem does lead to a formula. The Pythagorean theorem is a mathematical law about how a right triangle's sides are related to each other, which leads us to the formula a2 + b2 = c2. This formula will help us find the missing length of a right triangle's side if we know the lengths of the other two sides for any and all right triangles.

There are some formulas that appear frequently in algebra (distance formula, area formulas, etc). It's a good idea to memorize them by heart. Get to know them, ask about their families. You know...the yooj.

There are also unit conversion formulas which are crazy-useful to know in some problems (Celsius to Fahrenheit, meters to feet, etc.), but it's not absolutely necessary to memorize them.

Warning: Always know what the variables of a formula represent. Do whatever it takes. Seriously. Write out in the margin of your paper, "H stands for the area of half a circle" or something like that. It's a lot easier to answer questions correctly if you know the meanings of all the symbols you're using. Just as it's easier to avoid getting into a car accident when you know that that red octagonal sign means "stop."

Example 1

Jim gets paid $10 per hour. The amount Jim gets paid in a week depends on the number of hours he works that week. What's a formula that shows his pay p after working h hours?

Exercise 1

The formula for the area of a circle is A = πr2. What do the letters A and r represent?

Exercise 2

The formula for the area of a circle is  A = πr2. Which is the dependent and which is the independent variable?

Exercise 3

The formula for the area of a circle is A = πr2. Let H be the area of half a circle. Write a formula describing H in terms of r.

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