math help

What is 9/16 + 11/12?

What is 9/16 + 11/12?

This is how to add

9
16
 +
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 16 by 12 and get 192.

9/16 times 12

Do the same for the second term. We multiply 11 by 16, and get 176, then multiply 16 by 12 and get 192.

11/12 times 16

So now our fractions look like this:

108
192
 +
176
192

Step 2

Since our denominators match, we can add the numerators.

108 + 176 = 284

So the answer is:

284
192

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:

284
192
 ÷ 2 =
142
96

Let's try dividing by that again...

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

142
96
 ÷ 2 =
71
48

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...

No good. 53 is larger than 48. So we're done reducing.

There you have it! Here's the final answer to 9/16 + 11/12

9
16
 +
11
12
 =
71
48
© 2014 Randy Tayler

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