math help

What is 16/48 + 6/11?

What is 16/48 + 6/11?

Here's how we add

16
48
+
6
11

Step 1

We still have different denominators (bottom numbers), though, so we need to get a common denominator. This will make the bottom numbers match. Multiply the denominators together first. Now, multiply each numerator by the other term's denominator.

Now we multiply 16 by 11, and get 176, then we multiply 48 by 11 and get 528.

16/48 times 11

Now for the second term. You multiply 6 by 48, and get 288, then multiply 48 by 11 and get 528.

6/11 times 48

This gives us a new problem that looks like so:

176
528
+
288
528

Step 2

Since our denominators match, we can add the numerators.

176 + 288 = 464

That gives us an answer of

464
528

Step 3

Can this fraction be reduced?

First, we attempt to divide it by 2...

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

464
528
÷ 2 =
232
264

Let's try dividing by that again...

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

232
264
÷ 2 =
116
132

Let's try dividing by that again...

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

116
132
÷ 2 =
58
66

Let's try dividing by that again...

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

58
66
÷ 2 =
29
33

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...

No good. 31 is larger than 29. So we're done reducing.

There you have it! Here's the final answer to 16/48 + 6/11

16
48
+
6
11
=
29
33
© 2014 Randy Tayler