math help

What is 7/16 + 7/12?

What is 7/16 + 7/12?

Here's how to add

7
16
+
7
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 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 7 by 16, and get 112, then multiply 16 by 12 and get 192.

7/12 times 16

The problem now has new fractions to add:

84
192
+
112
192

Step 2

Since our denominators match, we can add the numerators.

84 + 112 = 196

This yields the answer

196
192

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:

196
192
÷ 2 =
98
96

Let's try dividing by that again...

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

98
96
÷ 2 =
49
48

Let's try dividing by that again...

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

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...

Nope! So now we try the next greatest prime number, 19...

Nope! So now we try the next greatest prime number, 23...

Nope! So now we try the next greatest prime number, 29...

Nope! So now we try the next greatest prime number, 31...

Nope! So now we try the next greatest prime number, 37...

Nope! So now we try the next greatest prime number, 41...

Nope! So now we try the next greatest prime number, 43...

Nope! So now we try the next greatest prime number, 47...

Nope! So now we try the next greatest prime number, 53...

No good. 53 is larger than 49. So we're done reducing.

There you have it! Here's the final answer to 7/16 + 7/12

7
16
+
7
12
=
49
48
© 2014 Randy Tayler