math help

What is 20/64 + 10/12?

What is 20/64 + 10/12?

Let's add

20
64
 +
10
12

Step 1

Of course, you can't add two fractions if the denominators (bottom numbers) don't match. To get a common denominator, multiply the denominators together. Then we fix the numerators by multiplying each one by their other term's denominator.

Now you multiply 20 by 12, and get 240, then we multiply 64 by 12 and get 768.

20/64 times 12

Do the same for the second term. We multiply 10 by 64, and get 640, then multiply 64 by 12 and get 768.

10/12 times 64

The problem now has new fractions to add:

240
768
 +
640
768

Step 2

Since our denominators match, we can add the numerators.

240 + 640 = 880

This yields the answer

880
768

Step 3

The last step is to reduce the fraction if we can.

To find out, we try dividing it by 2...

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

880
768
 ÷ 2 =
440
384

Now, try the same number again.

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

440
384
 ÷ 2 =
220
192

Now, try the same number again.

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

220
192
 ÷ 2 =
110
96

Now, try the same number again.

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

110
96
 ÷ 2 =
55
48

Now, try the same number again.

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

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...

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

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

No good. 53 is larger than 48. So we're done reducing.

Congratulations! Here's your final answer to 20/64 + 10/12

20
64
 +
10
12
 =
55
48
© 2014 Randy Tayler

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