math help

What is 40/41 + 4/12?

What is 40/41 + 4/12?

This is how to add

40
41
 +
4
12

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 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 4 by 41, and get 164, then multiply 41 by 12 and get 492.

4/12 times 41

This gives us a new problem that looks like so:

480
492
 +
164
492

Step 2

Since our denominators match, we can add the numerators.

480 + 164 = 644

That gives us an answer of

644
492

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:

644
492
 ÷ 2 =
322
246

Now, try the same number again.

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

322
246
 ÷ 2 =
161
123

Now, try the same number again.

Nope. Try the next prime number, 3...

Nope. Try the next prime number, 5...

Nope. Try the next prime number, 7...

Nope. Try the next prime number, 11...

Nope. Try the next prime number, 13...

Nope. Try the next prime number, 17...

Nope. Try the next prime number, 19...

Nope. Try the next prime number, 23...

Nope. Try the next prime number, 29...

Nope. Try the next prime number, 31...

Nope. Try the next prime number, 37...

Nope. Try the next prime number, 41...

Nope. Try the next prime number, 43...

Nope. Try the next prime number, 47...

Nope. Try the next prime number, 53...

Nope. Try the next prime number, 59...

Nope. Try the next prime number, 61...

Nope. Try the next prime number, 67...

Nope. Try the next prime number, 71...

Nope. Try the next prime number, 73...

Nope. Try the next prime number, 79...

Nope. Try the next prime number, 83...

Nope. Try the next prime number, 89...

Nope. Try the next prime number, 97...

Nope. Try the next prime number, 101...

Nope. Try the next prime number, 103...

Nope. Try the next prime number, 107...

Nope. Try the next prime number, 109...

Nope. Try the next prime number, 113...

Nope. Try the next prime number, 127...

No good. 127 is larger than 123. So we're done reducing.

Congratulations! Here's your final answer to 40/41 + 4/12

40
41
 +
4
12
 =
161
123
© 2014 Randy Tayler

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