Things You'll Need:
- paper and pencil
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Step 1
How do you add fractions? If both fractions have the same denominator, simply add the two numerators together and keep the same denominator. Then reduce the fraction. Look at these examples.
5/8 + 11/8 = 16/8 = 2
In this example, the numerators are 5 and 11. Add them together to get 16. Then divide by the denominator which is 8 since they share the same denominator. Then reduce 16/8 to 2.
1/18 + 7/18 = 8/18 = 4/9
Here the numerators are 1 and 7, which add up to 8. Then you divide by 18 since the denominator is the same. Then you reduce 8/18 to 4/9. -
Step 2
How do you multiply fractions? Multiplying fractions is one of the easiest operations to do with fractions. Write the fractions out next to each other. Then just multiply the numerators across the top. This will give you your new numerator. Then multiply the denominators across the bottom. This is your new denominator. Here's an example.
2/3 * 5/12
First multiply the numerators, so 2*5 = 10
Then multiply the denominators, so 3*12 = 36
So 10 is the numerator of your answer, and 36 is the denominator. The answer is 10/36. Then you must reduce your answer. In this case it reduces to 5/18. When you're learning how to multiply fractions, you will be doing a lot of reducing. The next step will help you with reducing fractions. -
Step 3
Learn to convert a fraction into a like fraction by reducing it or multiplying it by a factor. As an example, 1/2 is equal to one half, as long as the denominator is twice the numerator. So 1/2 = 2/4 = 3/6 = 4/8 and so on. In this way, you can manipulate a fraction to have whatever denominator you want, as long as it's a multiple of your original fraction. Just multiply top and bottom by the same number, and your fraction will be the same as the original. Here's another example.
2/3 times 1/1 = 2/3
2/3 times 2/2 = 4/6
2/3 times 3/3 = 6/9
And so on. These are all the same fraction. Being able to convert fractions like this will allow you to do fractions with different denominators. Notice that if you divide by 2/2 or 3/3 or 4/4 your numerator and denominator will get smaller. This is called reducing fractions. To reduce a fraction, simply divide top and bottom by the greatest common factor between the numerator and the denominator. Finding the greatest common factor is a subject for another article. -
Step 4
Adding fractions with different denominators should be easy now. First find the lowest common denominator of your fractions. There is a link at the bottom of this article in the resources section about how to find the lowest common denominator. Once you have your LCD, you use step 3 above to convert your original fractions into the form where their denominators are both the same and are both the lowest common denominator. Now that your fractions share a denominator, you can add them like in step 1. Here's an example.
3/7 + 4/5
The lowest common denominator is 35. Again, check the article in the resources for how to find the lowest common denominator. Next, convert both fractions to lowest common denominator form.
3/7 times 5/5 = 15/35
4/5 times 7/7 = 28/35
Now we can add the numerators since the denominators are the same. 15 + 28 = 43. This gives us our final numerator. The answer is 43/35. -
Step 5
How do you subtract fractions? Now that you know how to add fractions, subtracting fractions is easy. Simply follow the steps for addition, but subtract the numerators instead of adding them.
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Step 6
How do you divide fractions? Write out your fractions next to each other. The first fraction will be divided by the second fraction. Now, take the second fraction, and flip it over so that the numerator is on the bottom now, and the denominator is on the top now. This is called the reciprocal of the divisor fraction.
Now just multiply your first fraction by the reciprocal of the second fraction and you will have your answer. Here's an example.
11/20 divided by 2/5
Now just flip the 2/5 over into 5/2 and then multiply them.
11/20 * 5/2 = 55/40 Now reduce your fraction.
55/40 divided by 5/5 = 11/8 and there's your answer. -
Step 7
Now that you understand the basics, just practice using these operations on many fractions. Read some other articles on topics like reducing fractions, finding the greatest common factor, finding the least common denominator and you will quickly master fractions.
