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### Course: Arithmetic>Unit 13

Lesson 2: Visually adding and subtracting fractions

To add two fractions with different denominators, you need to find the least common multiple of the denominators. You can then rewrite both fractions with this common denominator, which will allow you to add the numerators together. In the example given, 5/6 and 1/4 are rewritten as 10/12 and 3/12, respectively, resulting in a sum of 13/12.

## Want to join the conversation?

• So you basically change both of the fraction's denominators and change them to something like 3/8+4/6 the denominator would be 24?
• Yes, because if you think of 8*? = 24 and 6*? = 24 then they can both be divisible by 24 and have no remainder. We can use division to help. 24 divided by 8 is 3, right? 24 divided by 6 is 4. This is called simplifying or it can also be called common denominators. Or LCM which stands for Least common multiple.
• At , why didn't the denominator change? Why didn't it stack up to 24 when 10 and 13 stacked up? I thought that what you do to the top, you must do the same to the bottom. So when you add the numerator, then shouldn't the denominator be changed as well?
OOF
• OOF indeed. Adding fractions doesn't add the two "divided by"s, or the denominators, simply the numerators. The denominators do stack up, however, just only in cases like (3/12)/12. Then that would be 3/24. Hope that helped, have a yeet-erific day :D
• how do i convert a fraction?
• To convert a fraction to a percentage or decimal, divide the numerator by the denominator to change the fraction to a decimal. Say you have "convert 3/6 to a percentage and a decimal." 3/6=0.5, so 3/6 as a decimal is 0.5. To turn it into a percentage, do 0.5*100. Now it's 50 or 50%
• How can you add 1/4 3/5 3/10?
• The first thing you would have to do is to change all of the denominators to a common denominator. To do this, find the lowest number that is divisible by all of your denominators. In this case, that number would be 100.

Then look at the numerator. To make sure that the fractions are still the same value, we need to change the numerator by the same amount we changed the denominator. So:

4 goes into 100 25 times. That means we need to also multiply the numerator by 25. That means that we now have 25/100 instead of 1/4. That means that 1/4 and 25/100 are the same value. We now do this for the other fractions.

5 goes into 100 20 times. So in this case we multiply the numerator by 20. 20 multiplied by 3 is 60. So instead of 3/5 we now have 60/100.

Finally, you need to do the last fraction. 10 goes into 100 10 times. So we need to do 3 multiplied by 10. Then we would get 30/100.

The last thing you have to do is add the numerators back together. Our denominators are now the same, so the new problem is this:

25/100 + 60/100 +30/100

Then we add the numerators, so we do 25+60+30. This comes out to be 115.

So our answer would be 115/100. But this is an improper fraction, so we could also change it into 1 and 15/100, because 100/100 is equal to one.

To simplify it, then we change it to 3/20 by dividing both 15 and 100 by 5.

Our final answer would be 1 and 3/20. Hope this helped!
• Why do we need to simplify ?
• Basically to make it look less daunting and easier to read
12345/24690 is the same as 1/2 but one is waaay harder to read than the other.
• how do i do this
• To add fractions, the number on the bottom (called the denominator) must be the same for both of the fractions. For example, to add 1/2 + 1/3, we need to get the denominators (the bottom numbers) to be the same. To do this, we find whats called the "least common denominator". An easy way to do this is to simply multiply those two denominators (2 and 3) and notice what you had to multiply each denominator by to get those numbers. So the denominator 2 had to be multiplied by 3 to get 6, and the denominator 3 had to multiplied by 2 to get 6. So we do the same with the top numbers. In this case, they are both 1 (1/2 +1/3) so the answer is 3/6 + 2/6 which is equal to 5/6. If you still need help, here is a Khan Academy video on this subject: https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-add-sub-fractions/v/adding-small-fractions-with-unlike-denominators
• Easy way to do it:

Let's say the problem is... you know what, 5/6 + 1/4.

So. Step one is to find the common denominator, which, in this case, is 12.

next, we see how many times 6 goes into 12, which is 2. now we take the top number, 5, and times it by 2, because if we are multiplying the denominator we have to multiply the numerator as well. so- 5x2 is ten. our new fraction is 10/12.
repeat this with the next fraction!
• yea thats basically sal's video compressed into a comment that took me 30 secs to read what is this doing but thanks anyways.
• how are they both equal
• Example: 3/4 is equal to 6/8. They are equal because 3 x 2=6 and 4 x 2=8. Another Example: 2/4 is equal to 1/2 because 2 divided by 2 =1 and 4 divided by 2 =2. as long as you multiply or divide both numbers by the same thing, they are equal. The same applies for mixed numbers and improper fractions. Hope that was helpful!
• Why there is 12
• The reason why the denominator changes, is because of this:
We can't add/subtract fractions that have different denominators. But, we can change the fractions so that they get the same denominator. This is done by finding a common multiple of the denominators.

Doing `5/6 + 1/4` in the video, `6` and `4` are the denominators.
So, go through the multiples of both denominator numbers. Then find a common multiple which will become a suitable denominator.
Multiples of `6`: `6,12,18,...`
Multiples of `4`: `4,8,12,16,...`
Look; there's a `12` in both. So, it's a common multiple, and we can use this as our denominator.

Our next step is to convert both fractions so that they have this denominator! Remember to multiply both the top and bottom by the same number so that it stays the same.
- In `5/6`, the denominator is `6` and we want it to be `12`. Multiply the top and bottom by `2` because `6*2 = 12`:
`(5*2)/(6*2) = 10/12`
- In `1/4`, the denominator is `4` and we want it to be `12`. Multiply the top and bottom by `3` because `4*3 = 12`:
`(1*3)/(4*3) = 3/12`

Now it's easy: add `10/12` and `3/12` together! Remember to leave the denominator alone.
`10/12 + 3/12 = (10 + 3)/12 = 13/12`

This might feel hard, but just practicing to familiarise yourself with the process will make this much quicker and easier, trust me! Hope it helps.
• Is the course challenge hard?