math help

What is 4/52 + 10/12?

What is 4/52 + 10/12?

Let's add

4
52
 +
10
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 10 by 52, and get 520, then multiply 52 by 12 and get 624.

10/12 times 52

The problem now has new fractions to add:

48
624
 +
520
624

Step 2

Since our denominators match, we can add the numerators.

48 + 520 = 568

The sum we get is

568
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:

568
624
 ÷ 2 =
284
312

Let's try dividing by that again...

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

284
312
 ÷ 2 =
142
156

Let's try dividing by that again...

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

142
156
 ÷ 2 =
71
78

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...

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...

No good. 73 is larger than 71. So we're done reducing.

There you have it! Here's the final answer to 4/52 + 10/12

4
52
 +
10
12
 =
71
78
© 2014 Randy Tayler

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