math help

What is 15/11 + 4/12?

What is 15/11 + 4/12?

Here's how to add

15
11
 +
4
12

Step 1

Of course, you can't add two fractions if the denominators (bottom numbers) don't match. To get a common denominator, multiply the denominators together. Then we fix the numerators by multiplying each one by their other term's denominator.

Now you multiply 15 by 12, and get 180, then we multiply 11 by 12 and get 132.

15/11 times 12

Do the same for the second term. We multiply 4 by 11, and get 44, then multiply 11 by 12 and get 132.

4/12 times 11

The problem now has new fractions to add:

180
132
 +
44
132

Step 2

Since our denominators match, we can add the numerators.

180 + 44 = 224

This yields the answer

224
132

Step 3

The last step is to reduce the fraction if we can.

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:

224
132
 ÷ 2 =
112
66

Let's try dividing by that again...

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

112
66
 ÷ 2 =
56
33

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...

No good. 37 is larger than 33. So we're done reducing.

There you have it! Here's the final answer to 15/11 + 4/12

15
11
 +
4
12
 =
56
33
© 2014 Randy Tayler

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