math help

What is 24/26 + 6/12?

What is 24/26 + 6/12?

Here's how you add

24
26
 +
6
12

Step 1

We can't add two fractions with different denominators (the bottom number). So you need to get a common denominator - both bottom numbers need to match. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 24 by 12, and get 288, then we multiply 26 by 12 and get 312.

24/26 times 12

Do the same for the second term. We multiply 6 by 26, and get 156, then multiply 26 by 12 and get 312.

6/12 times 26

So now our fractions look like this:

288
312
 +
156
312

Step 2

Since our denominators match, we can add the numerators.

288 + 156 = 444

Now we have an answer.

444
312

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

To find out, we try dividing it by 2...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

444
312
 ÷ 2 =
222
156

So far so good... let's try to divide by that number again.

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

222
156
 ÷ 2 =
111
78

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 3...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

111
78
 ÷ 3 =
37
26

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 5...

No good. So next you try the next prime number, which is 7...

No good. So next you try the next prime number, which is 11...

No good. So next you try the next prime number, which is 13...

No good. So next you try the next prime number, which is 17...

No good. So next you try the next prime number, which is 19...

No good. So next you try the next prime number, which is 23...

No good. So next you try the next prime number, which is 29...

No good. 29 is larger than 26. So we're done reducing.

And we're done! Here's the final answer to 24/26 + 6/12

24
26
 +
6
12
 =
37
26
© 2014 Randy Tayler

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