math help

What is 21/63 + 2/6?

What is 21/63 + 2/6?

Let's add

21
63
 +
2
6

Step 1

We can't add two fractions with different denominators (the bottom number). So you need to get a common denominator - both bottom numbers need to match. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 21 by 6, and get 126, then we multiply 63 by 6 and get 378.

21/63 times 6

Do the same for the second term. We multiply 2 by 63, and get 126, then multiply 63 by 6 and get 378.

2/6 times 63

So now our fractions look like this:

126
378
 +
126
378

Step 2

Since our denominators match, we can add the numerators.

126 + 126 = 252

Now we have an answer.

252
378

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

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:

252
378
 ÷ 2 =
126
189

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:

126
189
 ÷ 3 =
42
63

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

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

42
63
 ÷ 3 =
14
21

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...

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

14
21
 ÷ 7 =
2
3

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

No good. 7 is larger than 2. So we're done reducing.

And we're done! Here's the final answer to 21/63 + 2/6

21
63
 +
2
6
 =
2
3
© 2014 Randy Tayler

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