math help

What is 4/52 + 4/6?

What is 4/52 + 4/6?

This is how we add

4
52
 +
4
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 4 by 6, and get 24, then we multiply 52 by 6 and get 312.

4/52 times 6

Do the same for the second term. We multiply 4 by 52, and get 208, then multiply 52 by 6 and get 312.

4/6 times 52

The problem now has new fractions to add:

24
312
 +
208
312

Step 2

Since our denominators match, we can add the numerators.

24 + 208 = 232

This yields the answer

232
312

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:

232
312
 ÷ 2 =
116
156

Let's try dividing by that again...

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

116
156
 ÷ 2 =
58
78

Let's try dividing by that again...

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

58
78
 ÷ 2 =
29
39

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...

Nope! So now we try the next greatest prime number, 29...

Nope! So now we try the next greatest prime number, 31...

No good. 31 is larger than 29. So we're done reducing.

There you have it! Here's the final answer to 4/52 + 4/6

4
52
 +
4
6
 =
29
39
© 2014 Randy Tayler

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