math help

What is 21/63 + 6/12?

What is 21/63 + 6/12?

Here's how we add

21
63
 +
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 21 by 12, and get 252, then we multiply 63 by 12 and get 756.

21/63 times 12

Do the same for the second term. We multiply 6 by 63, and get 378, then multiply 63 by 12 and get 756.

6/12 times 63

The problem now has new fractions to add:

252
756
 +
378
756

Step 2

Since our denominators match, we can add the numerators.

252 + 378 = 630

The sum we get is

630
756

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:

630
756
 ÷ 2 =
315
378

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 3...

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

315
378
 ÷ 3 =
105
126

Let's try dividing by that again...

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

105
126
 ÷ 3 =
35
42

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

Are both the numerator and the denominator evenly divisible by 7? Yes! So we reduce it:

35
42
 ÷ 7 =
5
6

Let's try dividing by that again...

No good. 7 is larger than 5. So we're done reducing.

There you have it! Here's the final answer to 21/63 + 6/12

21
63
 +
6
12
 =
5
6
© 2014 Randy Tayler

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