math help

What is 78/10 + 5/6?

What is 78/10 + 5/6?

Let's add

78
10
 +
5
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 5 by 10, and get 50, then multiply 10 by 6 and get 60.

5/6 times 10

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

468
60
 +
50
60

Step 2

Since our denominators match, we can add the numerators.

468 + 50 = 518

Answer:

518
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:

518
60
 ÷ 2 =
259
30

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...

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

There you have it! Here's the final answer to 78/10 + 5/6

78
10
 +
5
6
 =
259
30
© 2014 Randy Tayler

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