math help

What is 4/7 + 6/12?

What is 4/7 + 6/12?

Let's add

4
7
 +
6
12

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 4 by 12, and get 48, then we multiply 7 by 12 and get 84.

4/7 times 12

Now for the second term. You multiply 6 by 7, and get 42, then multiply 7 by 12 and get 84.

6/12 times 7

This gives us a new problem that looks like so:

48
84
 +
42
84

Step 2

Since our denominators match, we can add the numerators.

48 + 42 = 90

So what's the answer so far?

90
84

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:

90
84
 ÷ 2 =
45
42

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:

45
42
 ÷ 3 =
15
14

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. 17 is larger than 15. So we're done reducing.

And we're done! Here's the final answer to 4/7 + 6/12

4
7
 +
6
12
 =
15
14
© 2014 Randy Tayler

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