math help

What is 30/50 + 6/12?

What is 30/50 + 6/12?

Here's how to add

30
50
 +
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 30 by 12, and get 360, then we multiply 50 by 12 and get 600.

30/50 times 12

Do the same for the second term. We multiply 6 by 50, and get 300, then multiply 50 by 12 and get 600.

6/12 times 50

The problem now has new fractions to add:

360
600
 +
300
600

Step 2

Since our denominators match, we can add the numerators.

360 + 300 = 660

This yields the answer

660
600

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:

660
600
 ÷ 2 =
330
300

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

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

330
300
 ÷ 2 =
165
150

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:

165
150
 ÷ 3 =
55
50

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...

Are both the numerator and the denominator evenly divisible by 5? Yes! So we reduce it:

55
50
 ÷ 5 =
11
10

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 7...

No good. So next you try the next prime number, which is 11...

No good. 11 is larger than 10. So we're done reducing.

And we're done! Here's the final answer to 30/50 + 6/12

30
50
 +
6
12
 =
11
10
© 2014 Randy Tayler

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