math help

What is 9/10 + 10/12?

What is 9/10 + 10/12?

This is how to add

9
10
 +
10
12

Step 1

We still have different denominators (bottom numbers), though, so we need to get a common denominator. This will make the bottom numbers match. Multiply the denominators together first. Now, multiply each numerator by the other term's denominator.

Now we multiply 9 by 12, and get 108, then we multiply 10 by 12 and get 120.

9/10 times 12

Now for the second term. You multiply 10 by 10, and get 100, then multiply 10 by 12 and get 120.

10/12 times 10

This gives us a new problem that looks like so:

108
120
 +
100
120

Step 2

Since our denominators match, we can add the numerators.

108 + 100 = 208

That gives us an answer of

208
120

Step 3

Can this fraction be reduced?

First, we attempt to divide it by 2...

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

208
120
 ÷ 2 =
104
60

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

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

104
60
 ÷ 2 =
52
30

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

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

52
30
 ÷ 2 =
26
15

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...

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. 17 is larger than 15. So we're done reducing.

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

9
10
 +
10
12
 =
26
15
© 2014 Randy Tayler

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