math help

What is 22/22 + 10/12?

What is 22/22 + 10/12?

This is how we add

22
22
 +
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 22 by 12, and get 264, then we multiply 22 by 12 and get 264.

22/22 times 12

Do the same for the second term. We multiply 10 by 22, and get 220, then multiply 22 by 12 and get 264.

10/12 times 22

The problem now has new fractions to add:

264
264
 +
220
264

Step 2

Since our denominators match, we can add the numerators.

264 + 220 = 484

This yields the answer

484
264

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:

484
264
 ÷ 2 =
242
132

Let's try dividing by that again...

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

242
132
 ÷ 2 =
121
66

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...

Are both the numerator and the denominator evenly divisible by 11? Yes! So we reduce it:

121
66
 ÷ 11 =
11
6

Let's try dividing by that again...

No good. 11 is larger than 6. So we're done reducing.

There you have it! Here's the final answer to 22/22 + 10/12

22
22
 +
10
12
 =
11
6
© 2014 Randy Tayler

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