math help

What is 40/41 + 6/12?

What is 40/41 + 6/12?

Let's add

40
41
 +
6
12

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 40 by 12, and get 480, then we multiply 41 by 12 and get 492.

40/41 times 12

Now for the second term. You multiply 6 by 41, and get 246, then multiply 41 by 12 and get 492.

6/12 times 41

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

480
492
 +
246
492

Step 2

Since our denominators match, we can add the numerators.

480 + 246 = 726

Answer:

726
492

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:

726
492
 ÷ 2 =
363
246

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:

363
246
 ÷ 3 =
121
82

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...

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...

Nope! So now we try the next greatest prime number, 59...

Nope! So now we try the next greatest prime number, 61...

Nope! So now we try the next greatest prime number, 67...

Nope! So now we try the next greatest prime number, 71...

Nope! So now we try the next greatest prime number, 73...

Nope! So now we try the next greatest prime number, 79...

Nope! So now we try the next greatest prime number, 83...

No good. 83 is larger than 82. So we're done reducing.

There you have it! Here's the final answer to 40/41 + 6/12

40
41
 +
6
12
 =
121
82
© 2014 Randy Tayler

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