math help

What is 78/10 + 6/12?

What is 78/10 + 6/12?

Let's add

78
10
 +
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 78 by 12, and get 936, then we multiply 10 by 12 and get 120.

78/10 times 12

Do the same for the second term. We multiply 6 by 10, and get 60, then multiply 10 by 12 and get 120.

6/12 times 10

The problem now has new fractions to add:

936
120
 +
60
120

Step 2

Since our denominators match, we can add the numerators.

936 + 60 = 996

This yields the answer

996
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:

996
120
 ÷ 2 =
498
60

Now, try the same number again.

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

498
60
 ÷ 2 =
249
30

Now, try the same number again.

Nope. Try the next prime number, 3...

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

249
30
 ÷ 3 =
83
10

Now, try the same number again.

Nope. Try the next prime number, 5...

Nope. Try the next prime number, 7...

Nope. Try the next prime number, 11...

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

Congratulations! Here's your final answer to 78/10 + 6/12

78
10
 +
6
12
 =
83
10
© 2014 Randy Tayler

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