Many people, even when they are naturally good at math, have a hard time with fractions. If you fall in this category, there is hope. By following these tips, you can learn how to perform basic math functions using fractions.
Numerator vs. Denominator
A fraction represents a part of a whole number. If you have one half (i.e., 1/2) of a pie, for example, the whole pie has been divided into two equal parts, one of which is missing. The number on the bottom of the fraction is the number of parts or the denominator. The top number is how many of the parts are present, or the numerator.
Any time you change a fraction, whether to prepare it for a sum or to get your final answer, you have to maintain the same ratio. That is, you have to do the same thing to the numerator that you do to the denominator. For example, if you want to expand 4/5 so that the denominator is 10, you have to multiply the denominator by 2. In order to come up with a fraction that represents the same number, you must also multiply the numerator by two. Your expanded fraction is thus 8/10.
Conversely, if you have finished your calculations and need to simplify your fraction, you must divide the numerator and denominator by the same number. If you end up with 12/16, you can divide both numbers by 4 and get 3/4 as your final answer.
Addition and Subtraction
Before you add fractions or subtract one fraction from another, they have to have the same denominator. The parts each whole is divided into has to be equal. After all, you wouldn’t take five strawberries and five watermelons and call it ten servings of fruit. You have to equalize the serving sizes in order to get an accurate answer, and that’s what you’re doing when you expand your fractions so that they have the same denominator.
Therefore, if you want to add 1/3 to 1/9, you first have to find a common denominator. This one is easy because multiplying 3 times 3 will give you 9, so you only have to change one of the fractions. 1/3 becomes 3/9. Then you just add the numerators, and your answer is 4/9. If one of your denominators is not a multiple of the other, you can find a common denominator by multiplying the two to get a number that is divisible by both.
Multiplication and Division
Multiplying fractions is very straightforward. You multiply the numerators, multiply the denominators, and simplify your answer if possible. For example, 2/3 times 1/2 is 2/6. To simplify, divide both the numerator and the denominator by 2, and you get an answer of 1/3.
Dividing fractions is a similar process with one extra step. Before you start, you flip the fraction by which you are dividing, and then you multiply the two. That is, 1/2 divided by 1/6 is really 1/2 times 6/1. This gives you 6/2, which simplifies into 3/1 or just 3.
You don’t have to be afraid of fractions. Once you understand the basics of how they work, calculating them can be a breeze.