How to Add Fractions

Fractions can seem awfully confusing at first, but I hope that the following information might clear up some of that confusion. Fractions are used in everyday life, as in "two thirds of the city feels that the school must be rebuilt", so to learn how to use it properly is not in vain. Although you probably aren't adding, subtracting, multiplying and dividing fractions on a day to day basis, every bit of information can one day come in handy.

With that let's start on some simple fractions.

2/3 can be read as two thirds, or 66 %. The numerator here is 2, while the denominator is 3.

1/10 can be read as one tenth, or 10 %. The numerator is 1, and the denominator is 10.

To find a fraction you see which part of the whole you want. If there are 1200 people in a town, and 600 go to church every Sunday then the fraction would be 600/1200. These are large numbers and we would want to simplify it. Every fraction can be simplified by dividing the top and the bottom with the same number. What is the greatest number divisible with both 600 and 1200? The answer is 600, so divide both the numerator and the denominator by 600 to get 1/2. This means that 50% of this town goes to church every Sunday.

Now let's say that in the neighboring town there are 2000 people, and only 800 go to church every Sunday. This would mean that 800/2000 are frequent church goers. Simplify this fraction by dividing both top and bottom 400 and get 2/5. In this town only 40 % goes to church every Sunday.

To learn how to add fractions we can use the fractions from the above example,

1/2 + 2/5

To add fractions the denominators - the bottom numbers - have to be equal. To make this happen we can multiply both top and bottom in both fractions by the same number, a number that would make the denominators the same. Look at the numbers 2 and 5. What is the lowest number that has both 2 and 5 as factors?

The number would be 10, which is 2*5, and 5*2. This again means that in the first fraction (1/2) you have to multiply both the top and bottom by 5, which will give you 5/10. In the second fraction you must multiply the top and bottom by 2, so you'll end up with 4/10.

When you have two fractions you want to add and they have the same denominator, you can accomplish this by adding the nominators together. Do not add the denominators.

5/10 + 4/10 = 9/10

The number one thing to remember here is to find a common denominator.

We can also look at a more practical example. Let's say that a wife eats 1/3 of a pie and a husband eats 3/5. How much of the total pie is eaten?

The smallest number with both denominators 3 and 5 is 15. Multiply top and bottom of 1/3 by 5 to get the wife's share of 5/15. Then multiply top and bottom of the husband's share by 3 to get 9/15. Then add the nominators together

5/15 + 9/15 = 14/15

This means that there would be 14/15 part of the pie left, which is a little under 7 %.