math help

What is 10/11 + 6/9?

What is 10/11 + 6/9?

Let's add

10
11
 +
6
9

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 10 by 9, and get 90, then we multiply 11 by 9 and get 99.

10/11 times 9

Do the same for the second term. We multiply 6 by 11, and get 66, then multiply 11 by 9 and get 99.

6/9 times 11

So now our fractions look like this:

90
99
 +
66
99

Step 2

Since our denominators match, we can add the numerators.

90 + 66 = 156

Now we have an answer.

156
99

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...

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

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

156
99
 ÷ 3 =
52
33

Let's try dividing by that again...

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 10/11 + 6/9

10
11
 +
6
9
 =
52
33
© 2014 Randy Tayler

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