 # What is 3/4 + 4/10? Here's how to add

 3 4
+
 4 10

## 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 3 by 10, and get 30, then we multiply 4 by 10 and get 40. Now for the second term. You multiply 4 by 4, and get 16, then multiply 4 by 10 and get 40. This gives us a new problem that looks like so:

 30 40
+
 16 40

## Step 2

Since our denominators match, we can add the numerators.

30 + 16 = 46

So what's the answer so far?

 46 40

## 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:

 46 40
÷ 2 =
 23 20

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 20. So we're done reducing.

There you have it! Here's the final answer to 3/4 + 4/10

 3 4
+
 4 10
=
 23 20
© 2014 Randy Tayler