math help

What is 15/11 + 10/12?

What is 15/11 + 10/12?

This is how to add

15
11
 +
10
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 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 10 by 11, and get 110, then multiply 11 by 12 and get 132.

10/12 times 11

So now our fractions look like this:

180
132
 +
110
132

Step 2

Since our denominators match, we can add the numerators.

180 + 110 = 290

So the answer is:

290
132

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:

290
132
 ÷ 2 =
145
66

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...

No good. 67 is larger than 66. So we're done reducing.

There you have it! Here's the final answer to 15/11 + 10/12

15
11
 +
10
12
 =
145
66
© 2014 Randy Tayler

10/12 + 1/2
10/12 - 1/2
10/12 + 1/3
10/12 - 1/3
10/12 + 2/3
10/12 - 2/3
10/12 + 1/4
10/12 - 1/4
10/12 + 2/4
10/12 - 2/4
10/12 + 3/4
10/12 - 3/4
10/12 + 1/5
10/12 - 1/5
10/12 + 2/5
10/12 - 2/5
10/12 + 3/5
10/12 - 3/5
10/12 + 4/5
10/12 - 4/5
10/12 + 1/6
10/12 - 1/6
10/12 + 2/6
10/12 - 2/6
10/12 + 3/6
10/12 - 3/6
10/12 + 4/6
10/12 - 4/6
10/12 + 5/6
10/12 - 5/6
10/12 + 1/7
10/12 - 1/7
10/12 + 2/7
10/12 - 2/7
10/12 + 3/7
10/12 - 3/7
10/12 + 4/7
10/12 - 4/7
10/12 + 5/7
10/12 - 5/7
10/12 + 6/7
10/12 - 6/7
10/12 + 1/8
10/12 - 1/8
10/12 + 2/8
10/12 - 2/8
10/12 + 3/8
10/12 - 3/8
10/12 + 4/8
10/12 - 4/8
10/12 + 5/8
10/12 - 5/8
10/12 + 6/8
10/12 - 6/8
10/12 + 7/8
10/12 - 7/8
10/12 + 1/9
10/12 - 1/9
10/12 + 2/9
10/12 - 2/9
10/12 + 3/9
10/12 - 3/9
10/12 + 4/9
10/12 - 4/9
10/12 + 5/9
10/12 - 5/9
10/12 + 6/9
10/12 - 6/9
10/12 + 7/9
10/12 - 7/9
10/12 + 8/9
10/12 - 8/9
10/12 + 1/10
10/12 - 1/10
10/12 + 2/10
10/12 - 2/10
10/12 + 3/10
10/12 - 3/10
10/12 + 4/10
10/12 - 4/10
10/12 + 5/10
10/12 - 5/10
10/12 + 6/10
10/12 - 6/10
10/12 + 7/10
10/12 - 7/10
10/12 + 8/10
10/12 - 8/10
10/12 + 9/10
10/12 - 9/10
10/12 + 1/11
10/12 - 1/11
10/12 + 2/11
10/12 - 2/11
10/12 + 3/11
10/12 - 3/11
10/12 + 4/11
10/12 - 4/11
10/12 + 5/11
10/12 - 5/11
10/12 + 6/11
10/12 - 6/11
10/12 + 7/11
10/12 - 7/11
10/12 + 8/11
10/12 - 8/11
10/12 + 9/11
10/12 - 9/11
10/12 + 10/11
10/12 - 10/11
10/12 + 1/12
10/12 - 1/12
10/12 + 2/12
10/12 - 2/12
10/12 + 3/12
10/12 - 3/12
10/12 + 4/12
10/12 - 4/12
10/12 + 5/12
10/12 - 5/12
10/12 + 6/12
10/12 - 6/12
10/12 + 7/12
10/12 - 7/12
10/12 + 8/12
10/12 - 8/12
10/12 + 9/12
10/12 - 9/12
10/12 + 10/12
10/12 - 10/12
10/12 + 11/12
10/12 - 11/12