math help

What is 9/32 + 10/12?

What is 9/32 + 10/12?

Here's how to add

9
32
 +
10
12

Step 1

Can you add yet? Nope! The denominators don't match. We need a common denominator. So next we take both denominators and multiply them. Next, take each numerator and multiply it by the denominator of the other term.

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

9/32 times 12

Now for the second term. You multiply 10 by 32, and get 320, then multiply 32 by 12 and get 384.

10/12 times 32

We now have a new problem, that looks like this:

108
384
 +
320
384

Step 2

Since our denominators match, we can add the numerators.

108 + 320 = 428

That gives us the sum, which is

428
384

Step 3

Now, do we need to simplify this fraction?

First, we attempt to divide it by 2...

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

428
384
 ÷ 2 =
214
192

Let's try dividing by that again...

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

214
192
 ÷ 2 =
107
96

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 3...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

Nope! So now we try the next greatest prime number, 11...

Nope! So now we try the next greatest prime number, 13...

Nope! So now we try the next greatest prime number, 17...

Nope! So now we try the next greatest prime number, 19...

Nope! So now we try the next greatest prime number, 23...

Nope! So now we try the next greatest prime number, 29...

Nope! So now we try the next greatest prime number, 31...

Nope! So now we try the next greatest prime number, 37...

Nope! So now we try the next greatest prime number, 41...

Nope! So now we try the next greatest prime number, 43...

Nope! So now we try the next greatest prime number, 47...

Nope! So now we try the next greatest prime number, 53...

Nope! So now we try the next greatest prime number, 59...

Nope! So now we try the next greatest prime number, 61...

Nope! So now we try the next greatest prime number, 67...

Nope! So now we try the next greatest prime number, 71...

Nope! So now we try the next greatest prime number, 73...

Nope! So now we try the next greatest prime number, 79...

Nope! So now we try the next greatest prime number, 83...

Nope! So now we try the next greatest prime number, 89...

Nope! So now we try the next greatest prime number, 97...

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

There you have it! Here's the final answer to 9/32 + 10/12

9
32
 +
10
12
 =
107
96
© 2014 Randy Tayler

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