math help

What is 15/11 + 6/10?

What is 15/11 + 6/10?

Here's how to add

15
11
 +
6
10

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 10, and get 150, then we multiply 11 by 10 and get 110.

15/11 times 10

Do the same for the second term. We multiply 6 by 11, and get 66, then multiply 11 by 10 and get 110.

6/10 times 11

The problem now has new fractions to add:

150
110
 +
66
110

Step 2

Since our denominators match, we can add the numerators.

150 + 66 = 216

This yields the answer

216
110

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:

216
110
 ÷ 2 =
108
55

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...

No good. 59 is larger than 55. So we're done reducing.

There you have it! Here's the final answer to 15/11 + 6/10

15
11
 +
6
10
 =
108
55
© 2014 Randy Tayler

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