Saturday, November 7, 2009

Fractions ~ 10 Reasons We Need Them

As a math teacher, I found fractions were a constant source of difficulty for students. However, they are extremely important. Whether adding fractions, changing them to decimals or percents, or finding equivalent fractions, the procedures must be learned. Here are the reasons why:

1. Not everything comes in wholes. The minute you cut something in half, you're dealing with a fraction. They can't be avoided.

2. When you eat half of a sausage pizza and then eat one-fourth of a pepperoni pizza, you've eaten three-fourths of a pizza. You have to add fractions. You need a common denominator.

3. Some decimals are fractions.  Unfortunately, they are not as accurate as fractions. If you share one-third of nine apples, you are sharing three apples. If you try to convert one-third to a decimal you get 0.3333333333... times 9 which will give you 2.999999.... apples. It just doesn't work as well.

4. If half of your pizza is covered with mushrooms and you eat half of that half, you've eaten one-fourth of the whole pizza. That's multiplying fractions (1/2 times 1/2).

5. If you have 6 pizzas and you divide them into three groups, you would have 2 pizzas in each group. That's regular division. But if you have 6 pizzas and you cut each into thirds, then you have 18 parts. That's division with fractions (6 divided by 1/3).

6. All percents are fractions with denominators of 100. Fifty percent is 50/100 which is 1/2. You can't use percents without using fractions.

7. Many of the above calculations can be done with a calculator that has a fraction function. But once you get to algebra, you need to add fractions that have variables. You can't add 2a/3b+4c/5d on a calculator.

8. If one person can paint a room in three hours and a second person can paint the same room in two hours, how long will it take them if they work together. This problem requires an algebraic knowledge of fractions. (It should take 1 hour and 12 minutes if they work together).

9. Reciprocals deal with fractions. In anything dealing with waves (trigonometry, music, light, sound, electricity, radio, microwave, x-rays, etc.) the frequency (Hz or hertz or cycles per second) and the period (time to complete one cycle or seconds per cycle) are reciprocals of each other.

10. Basic arithmetic (this includes fractions) is the foundation of grade school mathematics leading to algebra. Algebra is the foundation of high school mathematics leading to calculus. Calculus is the foundation of all higher level mathematics including topics such as Linear Algebra, Topology, Cryptology, Differential Equations, Function Theory, Number Theory, Chaos Theory, and Probability. These are the courses that lead to careers in Engineering, Medicine, Business, Meteorology, Education, Physics, Actuarial Sciences, and Cryptography, to mention a few. And to think, it all goes back to the simple fraction.

1 comment:

  1. I edited this post. I originally stated that decimals are fractions. Since I was focusing on fractions, I was not thinking of those decimals that are not fractions such as pi or square root of two. I apologize for this and want to thank for pointing out my mistake.