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# Trouble with fractions.

Why does 1/12 + 1/8 = 5/24?

Why does it not = 2/20 or 1/10?

Hi Bear,

1/12 + 1/8 = what?

1/2 + 1/2 = what?

Take an orange, cut it in half. How many halves are there? Two halves!

How many oranges are there? One orange.

Think deeply on this and you will know, without a shadow of a doubt that

1/2 + 1/2 does NOT equal (1+1)/(2+2) = 2/4 = 1/2

Instead when you put the two halves of the orange back together you get one orange

1/2 + 1/2 = (1+1)/2 = 2/2 = 1

BUT WHY?

That's a tough question, the best I can explain it here is by factoring two expressions for you.

The first time we'll factor oranges, to figure out that there are 3 oranges. I'll use * to mean MULTIPLY.

orange + orange + orange = 1*orange + 1*orange + 1*orange = (1+1+1) * orange = 3 * orange

The second time to figure out that 2 halves really do add together to make one whole

1/2 + 1/2 = 1*1/2 + 1* 1/2 = (1+1)*1/2 = 2/2 = 1

This is enough for now. Your question is the right question, keep asking, and think a little about what I've said here.

Hey Bear!

Here's another angle -- a pizza cut in ten pieces has a SMALLER slice than a pizza for 8.

In this scene, we're adding ANOTHER slice (1/12) to the 1/8 -- the total has to be bigger than 1/10.

Best wishes ...

1/12+1/8=5/24 because you need to find a common denoimator.  Unlike fractions cannnot be added until the denominators are alike.

1. By multiplying 1/12 by 2 the new fraction becomes 2/24.

2. Next you need to multiply the second fraction by 3 making that fraction 3/24.

3. Now that both fractions have the same demoninator you can add the top numbers together giving you the answer of 5/24.