Fraction Tips, Tricks and Shortcuts

Here are some ideas, shortcuts, tips and tricks that can speed up answering fractions problems.

Remember that a fraction is just a number which names a portion of something. For instance, instead of having a whole pie, a fraction says you have a part of a pie--such as a half of one or a fourth of one.

Two digits make up a fraction. The digit on top is known as the numerator. The digit on the bottom is known as the denominator. To remember which is which, just remember that “denominator” and “down” both start with a “d.” And the “downstairs” number is the denominator. So for instance, in ½, the numerator is the 1 and the denominator (or
“downstairs”) number is the 2.
●     It’s easy to add two fractions if they have the same denominator. Just add the digits on top, and leave the bottom one the same: 1/10+ 6/10 = 7/10.
●     It’s the same with subtracting fractions with the same denominator: 7/10 - 6/10 = 1/10.
●     Adding and subtracting fractions with different denominators is a little more complicated. First, you have to get the problem so that they do have the same denominators. The easiest way to do this is to multiply the denominators: For 2/5 + 1/2 multiply 5 by 2. Now you have a denominator of 10.
But now you have to change the top numbers too.
Since you multiplied the 5 in 2/5 by 2, you also multiply the 2 by 2, to get 4. So the first number is now 4/10. Since you multiplied the second number times 5, you also multiply its top number by 5, to get a final fraction of 5/10. Now you can add 5 and 4 together to get a final sum of 9/10.
●     To reduce a fraction to its simplest form: This means getting it to where the only common factor of the numerator and denominator is 1. Think of it this way: Numerators and denominators are brothers that must be treated the same. If you do something to one, you must do it to the other, or it’s just not fair. For instance, if you divide your numerator by 2, then you should also divide the denominator by the same.

Let’s take an example: The fraction 2/10 . This is not reduced to its simplest terms because there is a number that will divide evenly into both: the number 2. We want to make it so that the only number that will divide evenly into both is 1. What can we divide into 2 to get 1? The number 2, of course! Now to be “fair,” we have to do the same thing to the denominator:
Divide 2 into 10 and you get 5. So our new, reduced fraction is 1/5.
•     In some ways, multiplying fractions is the easiest of all: Just multiply the two top numbers and then multiply the two bottom numbers. For instance, with this problem:
2/5 X 2/3 you multiply 2 by 2 and get a top number of 4; then multiply 5 by 3 and get a bottom number of 15. Your answer is 4/15.
●     Dividing fractions is more involved, but still not too hard. You once again multiply, but only AFTER you have turned the second fraction upside-down. To divide ⅞ by ½, turn the ½ into 2/1, then multiply the top numbers and multiply the bottom numbers: ⅞ X
2/1 gives us 14 on top and 8 on the bottom.

Converting Fractions to Decimals
There are a couple of ways to become good at converting fractions to decimals. The fastest way is to memorize some basic fraction facts. Here are fractions that you should know:

1/100 is “one hundredth,” expressed as a decimal, it’s .01.
1/50 is “two hundredths,” expressed as a decimal, it’s .02.
1/25 is “one twenty-fifths” or “four hundredths,” expressed as a decimal, it’s .04.
1/20 is “one twentieth” or “”five hundredths,” expressed as a decimal, it’s .05.
1/10 is “one tenth,” expressed as a decimal, it’s .1.