math help

What is 9/32 + 11/12?

What is 9/32 + 11/12?

Let's add

9
32
 +
11
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 9 by 12, and get 108, then we multiply 32 by 12 and get 384.

9/32 times 12

Do the same for the second term. We multiply 11 by 32, and get 352, then multiply 32 by 12 and get 384.

11/12 times 32

So now our fractions look like this:

108
384
 +
352
384

Step 2

Since our denominators match, we can add the numerators.

108 + 352 = 460

So the answer is:

460
384

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:

460
384
 ÷ 2 =
230
192

Now, try the same number again.

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

230
192
 ÷ 2 =
115
96

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...

Nope. Try the next prime number, 83...

Nope. Try the next prime number, 89...

Nope. Try the next prime number, 97...

No good. 97 is larger than 96. So we're done reducing.

Congratulations! Here's your final answer to 9/32 + 11/12

9
32
 +
11
12
 =
115
96
© 2014 Randy Tayler

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