math help

What is 78/92 + 6/12?

What is 78/92 + 6/12?

This is how to add

78
92
 +
6
12

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 78 by 12, and get 936, then we multiply 92 by 12 and get 1104.

78/92 times 12

Do the same for the second term. We multiply 6 by 92, and get 552, then multiply 92 by 12 and get 1104.

6/12 times 92

So now our fractions look like this:

936
1104
 +
552
1104

Step 2

Since our denominators match, we can add the numerators.

936 + 552 = 1488

Now we have an answer.

1488
1104

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:

1488
1104
 ÷ 2 =
744
552

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:

744
552
 ÷ 2 =
372
276

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:

372
276
 ÷ 2 =
186
138

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:

186
138
 ÷ 2 =
93
69

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:

93
69
 ÷ 3 =
31
23

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...

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. 29 is larger than 23. So we're done reducing.

And we're done! Here's the final answer to 78/92 + 6/12

78
92
 +
6
12
 =
31
23
© 2014 Randy Tayler

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