Add 1/2,1/8,1/4 and 1/3

Answer 1

Hello!

First things first. We can't add fractions that don't have a common denominator. So.. lets make them have the same denominator!

To do this we should list out the multiples of the each denominator.

1/2 has a denominator of 2. The multiples 2 are... 2,4,6,8,10,12,14,16,18,20,22,24,... and so on (12th in list)

1/8 has a denominator of 8. The multiples 8 are... 8,16,24,32... and so on (3rd in list)

1/4 has a denominator of 4. The multiples 4 are... 4,8,12,16,20,24,28... and so on (6th in list)

1/3 has a denominator of 3. The multiples 3 are... 3,6,9,12,15,18,21,24,27... and so on (8th in list)

Multiples go on forever, but our goal here is to find the lowest multiple that is common between all of our denominators. This is called the Least Common Multiple. In our case it is 24.

Now we must convert all of our fractions so that they have denominator of 24. Here's a trick on how to do that. Do you see how I marked what number in the list 24 was? Well we need to multiply by 1 using that number in the list. So lets convert!

1/2 x (12/12) = 12/24 (Since 24 was 12th on the list, we are using 12/12 as our equivalent to 1)

1/8 x (3/3) = 3/24 (Since 24 was 3rd on the list, we are using 3/3 as our equivalent to 1)

1/4 x (6/6) = 6/24 (Since 24 was 6th on the list, we are using 6/6 as our equivalent to 1)

1/3 x (8/8) = 8/24 (Since 24 was 8th on the list, we are using 8/8 as our equivalent to 1)

Great! Now our denominators are the same! Lets add!

12/24 + 3/24 + 6/24 + 8/24 = 29/24

**This method is very thorough, as you do problems you will see short cuts. I encourage you to use those shortcuts but just know this is the bare bones of how to solve these types of problems. You will see that they are not too difficult in the end! :)