math help

What is 48/30 + 2/7?

What is 48/30 + 2/7?

This is how we add

48
30
+
2
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 48 by 7, and get 336, then we multiply 30 by 7 and get 210.

48/30 times 7

Now for the second term. You multiply 2 by 30, and get 60, then multiply 30 by 7 and get 210.

2/7 times 30

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

336
210
+
60
210

Step 2

Since our denominators match, we can add the numerators.

336 + 60 = 396

That gives us the sum, which is

396
210

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:

396
210
÷ 2 =
198
105

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:

198
105
÷ 3 =
66
35

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...

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...

No good. 37 is larger than 35. So we're done reducing.

There you have it! Here's the final answer to 48/30 + 2/7

48
30
+
2
7
=
66
35
© 2014 Randy Tayler