The Pythagorean Theorem is a Necessary Bore

Pythagorean Theorem

That Pythagoras. I’m sure many students would like to flick his ear for coming up with his Pythagorean Theorem. I wonder how many thousands, or millions, of hours of homework have been focused on finding the hypotenuse of a right triangle? How many kids have spent their time coming through a story problem to figure out that the three lengths given in the problem were parts of a right triangle, then working backwards to find the height of a building, or a tree?

Well, it’s not as hard as some may think. The Pythagorean Theorem is pretty simple. You can almost think of it as a recipe. You have certain ingredients that you need, some instructions on how to put together those ingredients, and the final outcome. So let’s try and look at it that way.

Pythagorean Theorem Formula

Ingredients: A right triangle – This is a triangle that has one 90 degree angle and 3 sides. (But, honestly, if you didn’t know that a triangle has 3 sides, you may need to review your geometric shapes before you take on this Pythagorean Theorem recipe.)

Length of Sides A and B – Sides A and B are the two shortest sides on the triangle. The leftover length for the longest side is the hypotenuse. A and B can be the same length, but they are not longer than the hypotenuse.

Recipe Directions:
Really, the directions for the Pythagorean Theorem would be the formula. A² + B² = C²

Plug in the length of sides A and B into the variables for A and B in the formula. C is the length of the hypotenuse, or the long side of the triangle. If A was 3 and B was 5, you would have: 3² +5² = C²

Now you square A and B to get: 9 + 25 = C²

If you add 9 and 25, you get: 34 = C²

Now you know that C² is equal to 34. So, to solve for C, you need to take the square root of both C² and 34. The square root of C² is C and the square root of 34 is 5.83.

Now we know that C = 5.83. So your right triangle has a hypotenuse of 5.83.

Pythagorean Theorem Calculator

You can check your work, and experiment with other lengths, with this Pythagorean Theorem Calculator.

Adding Fractions in School

Adding fractions is an everyday activity, not just for homework. But, you need to be able to get through your homework assignments to have a good understanding of the principals of fractions. First, you need to know the parts of a fraction and what they mean. Once you know what makes up a fraction, you can learn the steps for adding fractions. Finally, it's also important to know where adding fractions can be useful in real life.

The Anatomy of Fractions

When you look at a fraction, there are three basic parts. A top number, a bottom number, and that little line that separates them. That bottom number is called a denominator. The denominator is basically the total possible parts available. The top number is the numerator, it is the actual amount of parts that you have. So, when you look at a fraction like ¹/₈, 1 is the numerator and 8 is the denominator. If you have a pizza that you cut into 8 slices and you take one slice, you have 1 of the 8 slices for the whole pizza. You have a fraction of a pizza. It just so happens that you have ¹/₈ of a pizza.

Adding Fractions

The first step for adding fractions is to create like denominators. The denominators for each fraction must be the same to be able to add them properly. This can sometimes get tricky. To convert the fractions so that they have the same denominator, you can multiply the numerator and the denominator of the first fraction by the denominator of the second fraction. Then, you can multiply the numerator and denominator of the second fraction by the original denominator of the first fraction. This is sometimes called cross-multiplication. You can use online calculators to find the lowest common denominator that is used as well as the GCF Calculator. Once the two fractions are converted to have the same denominator, the numerators can be added. Example: ¹/₂ + ¹/₄ would need to use cross multiplication to convert the fractions so they have the same denominator. ¹/₂ becomes ⁴/₈ and ¹/₄ becomes ²/₈. Now your equation looks like: ⁴/₈+ ²/₈. The you now can add the numerators and the resulting answer is ⁶/₈. This can be simplified to ³/₄.

Adding Fractions in Your Daily Life

There are a lot of ways that you add fractions in real life. Many sales at department stores have a fraction. If you work construction or are working on DIY products around the house, you may need to add different lengths and many of these lengths will be fractions of an inch. There are other ways you can use your adding fractions skills in real life, for more examples, try this blog post about adding fractions in your daily life.

Adding Fractions Calculator

For more help with your skills at adding fractions, CalcuNation Online Calculators has an Adding Fractions Calculator to help you check your answers. There are other fractions calculator that can be found on that site as well.

Percentages in School

While some students may cringe at the thought of using percentages, it's important for them to understand just how often they are used, and in ways they may not even realize. While percentages are related to fractions, they are basically a way to use math to compare results, or to calculate a rate.

What are Percentages?

A percentage is derived from a common fraction. This fraction is set as an amount of one hundred. As a matter of fact, if you break down the word "percent", it really means "per hundred". If you have an understanding of fractions, you can convert a percent to a fraction. All you need to do is convert the fraction so that the denominator is 100. The resulting numerator will be the percentage. In the case of the fraction, ³⁰/₅₀, this would convert to ⁶⁰/₁₀₀. That means that ³⁰/₅₀ is saying the same as 30 is 60% of 50.

Percentages and Money

Another easy way to think of percentages is with money. Since every dollar is 100 cents, one cent is literally one percent of a dollar. For teachers, this can be an easy way to introduce students to the principals of percentages. Once students have a grasp of percentages in the use of finance, you can move on to more advanced lessons that involve loans, rates, and the interest.

Grades and Percentages

For most students, the most important place to apply percentages is in the form of grades. Since most homework assignments and tests have a certain value associated to them, or a set amount of questions, teachers will grade students by what percentage of questions they answered correctly. If a test has 80 questions, and the student answered 70 correct, they answered ⁶⁴/₈₀th's of the questions correctly. Converted to a percentage, this comes out to 80%.

Percentage Calculators

Whether you are a student, or a teacher, learning how to calculate percentages is obviously important for functioning in our society. As a resource to help learn more about percentages, try a APY Interest Calculator to practice how percentages are used in loans, grades, health, and even in nature. You can use some of the other online calculators to help with different math calculations you may use every day.

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