math help

What is 7/16 + 5/12?

What is 7/16 + 5/12?

Here's how you add

7
16
+
5
12

Step 1

We can't add two fractions with different denominators (the bottom number). So you need to get a common denominator - both bottom numbers need to match. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 7 by 12, and get 84, then we multiply 16 by 12 and get 192.

7/16 times 12

Do the same for the second term. We multiply 5 by 16, and get 80, then multiply 16 by 12 and get 192.

5/12 times 16

So now our fractions look like this:

84
192
+
80
192

Step 2

Since our denominators match, we can add the numerators.

84 + 80 = 164

So the answer is:

164
192

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

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:

164
192
÷ 2 =
82
96

Now, try the same number again.

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

82
96
÷ 2 =
41
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...

No good. 43 is larger than 41. So we're done reducing.

Congratulations! Here's your final answer to 7/16 + 5/12

7
16
+
5
12
=
41
48
© 2014 Randy Tayler