math help

What is 40/41 + 3/6?

What is 40/41 + 3/6?

This is how to add

40
41
 +
3
6

Step 1

Of course, you can't add two fractions if the denominators (bottom numbers) don't match. To get a common denominator, multiply the denominators together. Then we fix the numerators by multiplying each one by their other term's denominator.

Now you multiply 40 by 6, and get 240, then we multiply 41 by 6 and get 246.

40/41 times 6

Do the same for the second term. We multiply 3 by 41, and get 123, then multiply 41 by 6 and get 246.

3/6 times 41

The problem now has new fractions to add:

240
246
 +
123
246

Step 2

Since our denominators match, we can add the numerators.

240 + 123 = 363

This yields the answer

363
246

Step 3

The last step is to reduce the fraction if we can.

To find out, we try dividing it by 2...

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 + 3/6

40
41
 +
3
6
 =
121
82
© 2014 Randy Tayler

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