math help

What is 4/52 + 6/12?

What is 4/52 + 6/12?

Here's how we add

4
52
 +
6
12

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 4 by 12, and get 48, then we multiply 52 by 12 and get 624.

4/52 times 12

Do the same for the second term. We multiply 6 by 52, and get 312, then multiply 52 by 12 and get 624.

6/12 times 52

The problem now has new fractions to add:

48
624
 +
312
624

Step 2

Since our denominators match, we can add the numerators.

48 + 312 = 360

This yields the answer

360
624

Step 3

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

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

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

360
624
 ÷ 2 =
180
312

So far so good... let's try to divide by that number again.

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

180
312
 ÷ 2 =
90
156

So far so good... let's try to divide by that number again.

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

90
156
 ÷ 2 =
45
78

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 3...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

45
78
 ÷ 3 =
15
26

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 5...

No good. So next you try the next prime number, which is 7...

No good. So next you try the next prime number, which is 11...

No good. So next you try the next prime number, which is 13...

No good. So next you try the next prime number, which is 17...

No good. 17 is larger than 15. So we're done reducing.

And we're done! Here's the final answer to 4/52 + 6/12

4
52
 +
6
12
 =
15
26
© 2014 Randy Tayler

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