math help

What is 16/48 + 4/7?

What is 16/48 + 4/7?

Here's how you add

16
48
+
4
7

Step 1

Can you add yet? Nope! The denominators don't match. We need a common denominator. So next we take both denominators and multiply them. Next, take each numerator and multiply it by the denominator of the other term.

So, we multiply 16 by 7, and get 112, then we multiply 48 by 7 and get 336.

16/48 times 7

Now for the second term. You multiply 4 by 48, and get 192, then multiply 48 by 7 and get 336.

4/7 times 48

We now have a new problem, that looks like this:

112
336
+
192
336

Step 2

Since our denominators match, we can add the numerators.

112 + 192 = 304

Answer:

304
336

Step 3

Now, do we need to simplify this fraction?

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

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

304
336
÷ 2 =
152
168

Let's try dividing by that again...

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

152
168
÷ 2 =
76
84

Let's try dividing by that again...

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

76
84
÷ 2 =
38
42

Let's try dividing by that again...

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

38
42
÷ 2 =
19
21

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...

No good. 23 is larger than 19. So we're done reducing.

There you have it! Here's the final answer to 16/48 + 4/7

16
48
+
4
7
=
19
21
© 2014 Randy Tayler