Teach your kids arithmetic – Fractions, those heck!

Fractions Yuck! I could hear the shrieks coming from my students every time we entered the realm of these nasty little demons. Whenever we embarked on an area of ​​mathematics that required heavy work on fractions, the students acted as if we were entering Hades after an arduous river crossing of Acheron, led by the intrepid boatman Charon and his three-headed dog Cerberus. . . Oh! It was that bad.

However, in reality, these bugbears we call fractions are not as demonic as they seem. And when we consider how important they are in the study of all areas of mathematics, we had better give them their rightful place, and the respect they deserve. At early ages, children encounter these entities because they are inherently difficult to consider. Unlike whole numbers, which consist of one part, fractions (or rationals, as they are called) consist of two: the numerator, or top part, and the denominator, or bottom part. Almost everyone knows this. And these monsters are quite friendly when we do multiplication or division arithmetic (which won’t be discussed here, they’ll just have to wait until I write that article). However, add or subtract, we are now talking about serious business. Students would cringe at the thought of adding two fractions with unusually different denominators, not to mention three fractions with different backgrounds. I guess “bottom up” would not apply here.

In any case, truth be told: adding fractions is not difficult. We just need to get on a common playing field and by that I mean the common denominator. Specifically, we want the lowest common denominator, or GCD for short. Once we have the LCD, we do a quick conversion on the numerators and then add them. Case closed. However, getting to this LCD screen is what gives students the most trouble. You could now go into the method of obtaining the GCD by first decomposing each bottom into prime numbers, a process known as prime decomposition, and then obtaining the GCD by eliminating all distinct primes, as well as primes common to primes. . supreme power–ugh, I’m already getting confused by all this gibberish. Hey wait, isn’t there an easier way?

Yes. Fortunately, there is. Since most students learn to find a common denominator (though not necessarily the GCD) by multiplying the two funds, we will base our method on that procedure. The only problem with this method is that they may need to multiply two large numbers together. By big, I mean maybe 12 x 18 or 24 x 16. Most students have a calculator to fall back on, so this really isn’t an issue. (Though if they learn my techniques, they won’t need the calculator.)

Ok, let’s get to the nitty-gritty of this method. Let’s take a specific example. Suppose we need to add 5/18 and 5/12 together. First, we need to find the GCD of 12 and 18. Before multiplying these numbers, we need to note that the greatest common factor of 12 and 18 is 6. The greatest common factor, or GCD of two numbers, is the greatest number that divides equally to the two given numbers. To get the LCD, all we need to do is multiply the two given numbers, 12 x 18 = 216, and then divide this result by the LCD of 6, to get 216/6 = 36. Voila! The GCD of 12 and 18 is 36. No prime decompositions, no distinct primes, no concern for higher powers.

Finally, to add the two fractions, we need to multiply the numerators by an appropriate factor to get the fitted fraction. For example, since 36/18 = 2, we must multiply the 5 of 5/18 by 2 to get 5/18 = 10/36; similarly, since 36/12 = 3, we multiply 5 by 3 to get 15; so 5/12 = 15/36. Finally, 5/18 + 5/12 = 10/36 + 15/36 = 25/36.

Try this method of sizing, and I’m sure you won’t be taking any boat rides with Charon or Cerberus any time soon. Until next time…