math help

What is 5/100 + 10/12?

What is 5/100 + 10/12?

Let's add

5
100
 +
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 5 by 12, and get 60, then we multiply 100 by 12 and get 1200.

5/100 times 12

Now for the second term. You multiply 10 by 100, and get 1000, then multiply 100 by 12 and get 1200.

10/12 times 100

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

60
1200
 +
1000
1200

Step 2

Since our denominators match, we can add the numerators.

60 + 1000 = 1060

That gives us the sum, which is

1060
1200

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:

1060
1200
 ÷ 2 =
530
600

Now, try the same number again.

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

530
600
 ÷ 2 =
265
300

Now, try the same number again.

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

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

Are both the numerator and the denominator evenly divisible by 5? Yes! So we reduce it:

265
300
 ÷ 5 =
53
60

Now, try the same number again.

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...

Nope. Try the next prime number, 47...

Nope. Try the next prime number, 53...

Nope. Try the next prime number, 59...

No good. 59 is larger than 53. So we're done reducing.

Congratulations! Here's your final answer to 5/100 + 10/12

5
100
 +
10
12
 =
53
60
© 2014 Randy Tayler

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