math help

What is 78/10 + 1/6?

What is 78/10 + 1/6?

Here's how we add

78
10
 +
1
6

Step 1

Can you add yet? Nope! The denominators don't match. We need a common denominator. So next we take both denominators and multiply them. Next, take each numerator and multiply it by the denominator of the other term.

So, we multiply 78 by 6, and get 468, then we multiply 10 by 6 and get 60.

78/10 times 6

Now for the second term. You multiply 1 by 10, and get 10, then multiply 10 by 6 and get 60.

1/6 times 10

We now have a new problem, that looks like this:

468
60
 +
10
60

Step 2

Since our denominators match, we can add the numerators.

468 + 10 = 478

That gives us the sum, which is

478
60

Step 3

Now, do we need to simplify this fraction?

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

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

478
60
 ÷ 2 =
239
30

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. So next you try the next prime number, which is 19...

No good. So next you try the next prime number, which is 23...

No good. So next you try the next prime number, which is 29...

No good. So next you try the next prime number, which is 31...

No good. 31 is larger than 30. So we're done reducing.

And we're done! Here's the final answer to 78/10 + 1/6

78
10
 +
1
6
 =
239
30
© 2014 Randy Tayler

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