math help

What is 20/64 + 6/12?

What is 20/64 + 6/12?

Here's how we add

20
64
 +
6
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 6 by 64, and get 384, then multiply 64 by 12 and get 768.

6/12 times 64

The problem now has new fractions to add:

240
768
 +
384
768

Step 2

Since our denominators match, we can add the numerators.

240 + 384 = 624

The sum we get is

624
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:

624
768
 ÷ 2 =
312
384

Let's try dividing by that again...

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

312
384
 ÷ 2 =
156
192

Let's try dividing by that again...

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

156
192
 ÷ 2 =
78
96

Let's try dividing by that again...

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

78
96
 ÷ 2 =
39
48

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 3...

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

39
48
 ÷ 3 =
13
16

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

Nope! So now we try the next greatest prime number, 11...

Nope! So now we try the next greatest prime number, 13...

Nope! So now we try the next greatest prime number, 17...

No good. 17 is larger than 13. So we're done reducing.

There you have it! Here's the final answer to 20/64 + 6/12

20
64
 +
6
12
 =
13
16
© 2014 Randy Tayler

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