math help

What is 6/10 + 10/12?

What is 6/10 + 10/12?

This is how we add

6
10
 +
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 6 by 12, and get 72, then we multiply 10 by 12 and get 120.

6/10 times 12

Do the same for the second term. We multiply 10 by 10, and get 100, then multiply 10 by 12 and get 120.

10/12 times 10

The problem now has new fractions to add:

72
120
 +
100
120

Step 2

Since our denominators match, we can add the numerators.

72 + 100 = 172

The sum we get is

172
120

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:

172
120
 ÷ 2 =
86
60

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:

86
60
 ÷ 2 =
43
30

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...

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...

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

No good. So next you try the next prime number, which is 13...

No good. So next you try the next prime number, which is 17...

No good. So next you try the next prime number, which is 19...

No good. So next you try the next prime number, which is 23...

No good. So next you try the next prime number, which is 29...

No good. So next you try the next prime number, which is 31...

No good. 31 is larger than 30. So we're done reducing.

And we're done! Here's the final answer to 6/10 + 10/12

6
10
 +
10
12
 =
43
30
© 2014 Randy Tayler

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