math help

What is 6/7 + 6/10?

What is 6/7 + 6/10?

Let's add

6
7
 +
6
10

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 6 by 10, and get 60, then we multiply 7 by 10 and get 70.

6/7 times 10

Now for the second term. You multiply 6 by 7, and get 42, then multiply 7 by 10 and get 70.

6/10 times 7

This gives us a new problem that looks like so:

60
70
 +
42
70

Step 2

Since our denominators match, we can add the numerators.

60 + 42 = 102

So what's the answer so far?

102
70

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:

102
70
 ÷ 2 =
51
35

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

No good. 37 is larger than 35. So we're done reducing.

And we're done! Here's the final answer to 6/7 + 6/10

6
7
 +
6
10
 =
51
35
© 2014 Randy Tayler

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