How to Add Fractions
If you want to learn how to add fractions, you came to the right place. Below are easy steps that will help you understand the process as well as have a general idea about the topic. But before starting with the steps, you need to know the basic concepts about add fractions. A fraction (from the Latin fractus, broken) is a number that can represent part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today (½, ⅝, ¾, etc.) and which consist of a numerator and a denominator. Adding fractions sometimes seem very complicated but that is only at first, so, lets make it easy.
Easy Steps to Add Fractions
Below are simple steps to learn how to add fractions. Go step by step, and check your progress.
- Let's start with these three words that we should define at the beginning:
1- Numerator - the top part of the fraction, and representing a number of equal parts
2- Denominator - the bottom part of the fraction, and telling how many of those parts make up a whole.
For example, for the fraction 2/3:
- is the numerator
- is the denominator.
3- LCD - lowest common denominator - the smallest number that all the different fractions' deminators will go into without giving you a remainder. See the example, for the fractions:
1/3 + 1/4 + 1/5
As you see here, there are 3 denominators: 3, 4, and 5. The LCD for these is 60. 3, 4 and 5 all go into 60 without creating a remainder.
There are other common denominators for 3, 4 and 5, including 120 and 240, but these are larger than 60, so they are not the LCD.
Hint: A quick way to find the LCD is to multiply the denominators together. However, sometimes this just creates a larger common denominator than the LCD, in which case you'll have to reduce the final fraction in your answer.
- Let's talk about the denominators when they are all the same.
When all the denominators are the same, it's easy: Add up all the numerators, and put them over the same denominator.
See the example:
1/12 + 3/12 + 5/12
= 9/12, which you can reduce to 3/4
2/17 + 3/17 + 10/17
It's easy, right?
- Now let's talk about the denominators when they are different.
Okay, here's where it gets a little trickier--but don't panic! Just follow this procedure. Let's start with an example:
1/3 + 2/9 + 3/10
1- Find the LCD for all the denominators.
For 3, 9 and 10, the LCD seems to be 90. All 3 numbers go evenly into 90 without a remainder.
2- For each of the denominators, find out how many times it goes into the LCD.
For 3: 3 goes into 90 30 times
For 9: 9 goes into 90 10 times
For 10: 10 goes into 90 9 times
3- For each of the original fractions, multiply the numbers you get in (2) to both the numerator and the denominator.
1/3 + 2/9 + 3/10 becomes
(1x30)/(3x30) + (2x10)/(9x10) + (3x9)/(10x9)
which, if you multiply out the numerators and denominators, becomes:
30/90 + 20/90 + 27/90
WAIT! Now they all have the same denominator! You can apply the procedure in the gray box above now:
Here your answer like a sunshine!
Practice makes perfect, don't hesistate to practice to achieve the desired goal. Try to combine the steps above with the video below in order to obtain the most information about how to add fractions.
How to Add Fractions Video
Below is also a video to help you learn how to Add Fractions.
We hope the above steps and video about how to add fractions have helped you in your quest to learn how to add fractions. If you like this page you might also want to go to our main page and learn more about our Book of the Worlds.