math help

What is 24/26 + 2/12?

What is 24/26 + 2/12?

Let's add

24
26
 +
2
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 2 by 26, and get 52, then multiply 26 by 12 and get 312.

2/12 times 26

So now our fractions look like this:

288
312
 +
52
312

Step 2

Since our denominators match, we can add the numerators.

288 + 52 = 340

So the answer is:

340
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:

340
312
 ÷ 2 =
170
156

Now, try the same number again.

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

170
156
 ÷ 2 =
85
78

Now, try the same number again.

Nope. Try the next prime number, 3...

Nope. Try the next prime number, 5...

Nope. Try the next prime number, 7...

Nope. Try the next prime number, 11...

Nope. Try the next prime number, 13...

Nope. Try the next prime number, 17...

Nope. Try the next prime number, 19...

Nope. Try the next prime number, 23...

Nope. Try the next prime number, 29...

Nope. Try the next prime number, 31...

Nope. Try the next prime number, 37...

Nope. Try the next prime number, 41...

Nope. Try the next prime number, 43...

Nope. Try the next prime number, 47...

Nope. Try the next prime number, 53...

Nope. Try the next prime number, 59...

Nope. Try the next prime number, 61...

Nope. Try the next prime number, 67...

Nope. Try the next prime number, 71...

Nope. Try the next prime number, 73...

Nope. Try the next prime number, 79...

No good. 79 is larger than 78. So we're done reducing.

Congratulations! Here's your final answer to 24/26 + 2/12

24
26
 +
2
12
 =
85
78
© 2014 Randy Tayler

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