Adding and Subtracting Fractions

Regular, Mixed, and Irregular Fractions

By Priyanka and Ethan

How to add regular fractions

Lets start off with this equation.

3/4 + 5/6

The first thing we have to do is find an even denominator. The denominator is the bottom number. The reason we need to do this, is so that the numbers can be compared evenly. The way you find an even denominator, is by finding a number they are both multiples of. You can find this by multiplying the denominators and then simplifying it. The common denominator for these fraction would be 12. Also, whatever you do to the denominator, you do to the numerator, so the equation would now look like this.

9/12 + 10/12 =

Then add the fractions together.

19/12.

If there is an irregular fraction like this one, you have to convert it into a whole number by finding out how many times the numerator goes into the denominator and how much is left over. The way you find out how many times the numerator goes into the denominator, Is by subtracting the denominator from the numerator until you cannot subtract it anymore. This would be your final answer:

1 7/12

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As you can see in this picture, There are the numbers 4 and 3. The common denominator is 12. The way you find this out, is by multiplying the 2 denominators together ( 4 x 3 = 12). If the number is too big and it still fits the both numbers, you can divide it by two if it is an even number.

How to add Improper fractions

Improper fractions are a lot like regular fractions. The difference between improper and regular, is that the numerator is bigger than the denominator, you are going to have to turn it into a mixed fraction. Say this is your problem:


7/2 + 9/10


The first thing you always do in a fractions equation, is find a common denominator. The way you do that is by finding a number they are both multiples of. 2 is a multiple of ten, and the other fraction already has a denominator of ten, so you can just bring up 7/2 to a denominator of ten.


35/20 + 9/10


Before you get confused here, what I did was just making the numerator up to the same scale as the denominator. I had to multiply the denominator by 5, so I also multiply the numerator by five giving me 35. The Next thing I have to to is add the fractions together so that will look like this:


35/20 + 9/10 = 44/10.


The next thing I have to do Is convert it into a mixed fraction with whole numbers. The way you do that is by finding out how many times 10 goes into 44. It goes in four times, and that means there is going to be a whole number of 4. The number left over from 44 is going to be four, so our final answer is going to be 4 4/10. We can actually simplify it because it can be split into two and you always want it to be as simple as possible, so the final answer would be :


4 2/5

How to add mixed Fractions

To add mixed fractions, Is like adding improper fractions. All we need to do Is convert it, and then convert it back. I will show you how to to that. Lets say our problem is this:


2 2/7 + 1 3/4


The first thing we need to do is convert the numbers into improper fractions so that they can be added as regular fractions. The way to do this, is by first multiplying the denominator by the amount of wholes, and then adding the numerator. For the first fraction ( 2 2/7 ), you would multiply 7 by 2 to get 14, and then adding the numerator 2, giving you an answer of 16/7. For the next one, 1 3/4, you would multiply 4 by 1 to get four, and then add three. The fraction would be 7/4. Then you add the fractions together:


16/7 + 7/4


But before you add, you need to find a common denominator. The way to do that, is by finding a number they are both multiples of. The way you do that, is by either writing out the multiples or multiplying the two denominators and then simplifying the number. In this case, the even denominator would be 28. The numbers would then have to be sized up the same amount as the denominators. For the first fraction ( 16/7 ), it would be multiplied by four so 16 x 4 = 64. For the next number 7/4, you have to multiply by seven so 7 x 7 = 49.


49/28 + 64/28 = 113/28.


The way we now turn this fraction back into a mixed fraction, is by finding out how many times the denominator goes into the numerator. It goes in 4 times, so there would be 4 wholes. There is 1 left over, so the final answer would be:


4 1/28

The second method, is where you add the whole numbers and then the fractions and add them together. there is a video to explain it.
How to add improper fractions

How to Subtract Regular Fractions:

Subtracting fractions can be similar to adding fractions; however, you are still subtracting. We will be using the equation below.
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Start off by finding a common denominator or the lowest common multiple (LCM for short). You can either list out all of the multiples of each denominator OR multiply the denominators. I will show you the first method of listing the multiples.
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As you can see above, the common denominator is 24. In order to get from 6 to 24 (for the first fraction), you multiply 6 by 4.


Remember this rule:

WHATEVER YOU DO TO THE BOTTOM, YOU DO TO THE TOP.


This means that if you multiply the denominator by one number, you must do the same operation to the numerator. This means that the numerator is now 20.


Look at the second fraction, the denominator is 8. You multiply 8 by 3 to get 24. You multiply the numerator (3) by 3 as well and you should get 9. Your new equation should be 20/24 - 9/24. All you have to do is subtract!


20/24 - 9/24

= 11/24

As you can see you can't simplify this fraction so that is your final answer!

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Welcome To: Subtracting Regular Fractions!

How to Subtract Mixed Fractions:

The basic concept of subtracting mixed fractions is the same when it comes to finding the common denominator and then simplifying the answer at the end. The only difference is that you have to convert the mixed fraction into an improper fraction.
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Start off by converting your mixed number into an improper fraction. In order to do this, all you have to do is multiply the denominator by the whole number and then add the numerator.
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Just like before, all you need to do is find a common denominator; in this case it is 18.


You multiply 9 by 2 to get 18; which is why you should multiply by the numerator (29) by 2 to get 58.

For the second fraction, you multiply 6 by 3 to get 18; which is why you should multiply by the numerator (17) by 3 to get 51.

The new equation is...

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In this case I didn't have to simplify my answer or convert it back into a mixed number but it can happen so this is just a heads up for that!
Welcome To: Subtracting Mixed Fractions!

How to Subtract Improper Fractions:

This is exactly like the "How to Subtract Mixed Fractions" tutorial above; however, without the whole converting the fractions from a mixed number to and improper fraction. It is easier and faster than subtracting mixed numbers.
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Let's start off with finding the common denominator. Like before, you can either list out the multiples or just multiply the two denominators. In this case I will do both to further extend your understanding.
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This next picture will show you the new equation and then how to solve the equation
Your answer is down below. Don't forget to simply and convert your final answer into a mixed fraction if you have to...
Welcome To: Subtracting Improper Fractions!