math help

What is 10/12 + 1/9?

What is 10/12 + 1/9?

Here's how we add

10
12
+
1
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 12 by 9 and get 108.

10/12 times 9

Do the same for the second term. We multiply 1 by 12, and get 12, then multiply 12 by 9 and get 108.

1/9 times 12

So now our fractions look like this:

90
108
+
12
108

Step 2

Since our denominators match, we can add the numerators.

90 + 12 = 102

So the answer is:

102
108

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:

102
108
÷ 2 =
51
54

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 3...

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

51
54
÷ 3 =
17
18

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 5...

No good. So next you try the next prime number, which is 7...

No good. So next you try the next prime number, which is 11...

No good. So next you try the next prime number, which is 13...

No good. So next you try the next prime number, which is 17...

No good. So next you try the next prime number, which is 19...

No good. 19 is larger than 17. So we're done reducing.

And we're done! Here's the final answer to 10/12 + 1/9

10
12
+
1
9
=
17
18
© 2014 Randy Tayler