math help

What is 72/63 + 3/6?

What is 72/63 + 3/6?

Here's how we add

72
63
 +
3
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 72 by 6, and get 432, then we multiply 63 by 6 and get 378.

72/63 times 6

Do the same for the second term. We multiply 3 by 63, and get 189, then multiply 63 by 6 and get 378.

3/6 times 63

So now our fractions look like this:

432
378
 +
189
378

Step 2

Since our denominators match, we can add the numerators.

432 + 189 = 621

So the answer is:

621
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...

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:

621
378
 ÷ 3 =
207
126

Let's try dividing by that again...

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

207
126
 ÷ 3 =
69
42

Let's try dividing by that again...

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

69
42
 ÷ 3 =
23
14

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...

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...

No good. 17 is larger than 14. So we're done reducing.

There you have it! Here's the final answer to 72/63 + 3/6

72
63
 +
3
6
 =
23
14
© 2014 Randy Tayler

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