We hear the groans through cyberspace. Why do certain people freeze at the thought of working with fractions” These frisky little fellows are a part of everyday life, and you come in contact with them constantly, whether you realize it or not. Especially those of us in the U.S. who are determined to hang on to the traditional British System of measurement in lieu of the more modern, decimal-loving Système International, better known as the Metric System.
If fractions confuse you, you are definitely not alone. Back in the spring of 2001, the Securities and Exchange Commission mandated that all U.S. trading markets fully “decimalize” all option and stock trading. The reasoning behind ridding the trading markets of those pesky fractions” The government agency believed that fractions were more difficult for the individual investor to comprehend and use. In their estimation:
decimals => better understanding + more trading & competition => $$$
(Money really does make the world go ‘round.) This mathematical move brought the U.S. up to speed with all other major exchanges around the world. Talk about peer pressure! But we digress…
All we’re going to do in this first “lesson” is talk about…
- 1) fractions in general,
- 2) fractions in particular, and
- 3) adding and subtracting
…basic stuff that many people have forgotten since their grade school days. Hopefully this information will resurface as positive repressed memories, unless your 4th-grade math teacher tended to hurl chalk and erasers your way on a daily basis… Uh oh, we’ve revealed too much.
What is a fraction” A portion of something, most commonly thought of in visual terms as a piece of a pie (or pizza in this fast-food world of ours – who makes pie anymore”). In the design industry, we think of it most commonly in terms of a fraction of an inch, a unit a measurement that we must work with all the time:
- How thick can that laminated glass be to fit into the existing frame” 1/2 inch
- How wide must a handrail / grab bar be in order to comply with the Americans with Disabilities Act [ADA]” 1-1/4 inches to 1-1/2 inches
- How thick should that countertop edge be for satisfying visual weight” 1-7/8 inch
- How wide must the molding be to cover those horribly uneven panel joints” 1-3/8 inches
- What’s the maximum vertical level change allowed per ADA guidelines if no beveling is used” 1/4 inch
- How thick will that that drywall partition be if we use our typical construction methods” 3-3/4 inches
You can ascertain how critical fractions can be. Not only might they add subtleties to and determine the restrictions of our designs, but they can also be critical to the health, safety and welfare of those who occupy the spaces and objects we create.
A fraction has a top number and bottom number. The fancy names for those parts of a fraction are the numerator and the denominator, respectively. The denominator is the one everyone gets up in arms about because it is the one that must be manipulated in order for most addition and subtraction to take place.
But before we get to the good stuff, let’s look at one more basic concept: the number “1” is whole, but it can be made up of an infinite number of fractions. For those of you in the States, first think of it as a dollar.
That’s why that coin you use to buy a newspaper is even called a quarter in the first place. Ah ha!
The idea goes for all other numbers as well:
For this reason, you can change a fraction’s numerator and denominator as long as you multiply or divide both numbers in the same way:
This concept will be critical when adding and subtracting, but it also makes an impact when grasping the fact that fractions can be represented in a couple of ways:
To make it a little tougher…
Can you now see why”
We hope you just had that Eureka! moment. If so, you’re ready to move on and get down to business.
3) Additions & Subtractions
The most basic addition examples:
Making it a little more complicated, what if we needed to add:
We would need to find “the least common denominator” for both fractions. In this case, the easiest thing to do would be to multiply 2 and 9 together to get 18 – that way, you’ll know that each of those numbers will then divide into 18.
Now let’s say we just needed to add:
Since 4/5 is the exact same thing as 8/10 (we multiplied both the numerator and the denominator by 2 to find a common denominator of 10), then…
All of the rules that we’ve just learned (or reminded ourselves of) that apply to addition apply the same exact way to subtraction. So let’s just take one more example to get the point across.
In this case, you could multiply 8 and 6 to find a common denominator of 48, but that’s not the least common denominator. The least common denominator is 24 (1/2 of 48) because 8 will divide into 24 three times and 6 will divide into 24 four times. However, it really doesn’t matter how you do it as long as you get the right answer, don’t you think” So…
You say poTAto, we say poTAHto. Whatever it takes to get you to the solution, baby.
More To Come
Amazingly enough, multiplication and division of fractions are easier than addition and subtraction. We’ll be covering those topics soon. For now, just relax, deal with all those repressed math memories and go enjoy yourself a 1/8th of a homemade pie and 1-3/4 cups of coffee.