math help

What is 70/51 + 10/12?

What is 70/51 + 10/12?

This is how we add

70
51
 +
10
12

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 70 by 12, and get 840, then we multiply 51 by 12 and get 612.

70/51 times 12

Now for the second term. You multiply 10 by 51, and get 510, then multiply 51 by 12 and get 612.

10/12 times 51

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

840
612
 +
510
612

Step 2

Since our denominators match, we can add the numerators.

840 + 510 = 1350

That gives us the sum, which is

1350
612

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:

1350
612
 ÷ 2 =
675
306

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:

675
306
 ÷ 3 =
225
102

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

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

225
102
 ÷ 3 =
75
34

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. 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. So next you try the next prime number, which is 37...

No good. 37 is larger than 34. So we're done reducing.

And we're done! Here's the final answer to 70/51 + 10/12

70
51
 +
10
12
 =
75
34
© 2014 Randy Tayler

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