math help

What is 72/63 + 10/12?

What is 72/63 + 10/12?

This is how we add

72
63
 +
10
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 72 by 12, and get 864, then we multiply 63 by 12 and get 756.

72/63 times 12

Now for the second term. You multiply 10 by 63, and get 630, then multiply 63 by 12 and get 756.

10/12 times 63

This gives us a new problem that looks like so:

864
756
 +
630
756

Step 2

Since our denominators match, we can add the numerators.

864 + 630 = 1494

So what's the answer so far?

1494
756

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:

1494
756
 ÷ 2 =
747
378

Now, try the same number again.

Nope. Try the next prime number, 3...

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

747
378
 ÷ 3 =
249
126

Now, try the same number again.

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

249
126
 ÷ 3 =
83
42

Now, try the same number again.

Nope. Try the next prime number, 5...

Nope. Try the next prime number, 7...

Nope. Try the next prime number, 11...

Nope. Try the next prime number, 13...

Nope. Try the next prime number, 17...

Nope. Try the next prime number, 19...

Nope. Try the next prime number, 23...

Nope. Try the next prime number, 29...

Nope. Try the next prime number, 31...

Nope. Try the next prime number, 37...

Nope. Try the next prime number, 41...

Nope. Try the next prime number, 43...

No good. 43 is larger than 42. So we're done reducing.

Congratulations! Here's your final answer to 72/63 + 10/12

72
63
 +
10
12
 =
83
42
© 2014 Randy Tayler

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