math help

What is 10/3 + 6/10?

What is 10/3 + 6/10?

Let's add

10
3
 +
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 10 by 10, and get 100, then we multiply 3 by 10 and get 30.

10/3 times 10

Now for the second term. You multiply 6 by 3, and get 18, then multiply 3 by 10 and get 30.

6/10 times 3

This gives us a new problem that looks like so:

100
30
 +
18
30

Step 2

Since our denominators match, we can add the numerators.

100 + 18 = 118

So what's the answer so far?

118
30

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:

118
30
 ÷ 2 =
59
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 10/3 + 6/10

10
3
 +
6
10
 =
59
15
© 2014 Randy Tayler

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