math help

What is 78/10 + 7/8?

What is 78/10 + 7/8?

Here's how you add

78
10
+
7
8

Step 1

Can you add yet? Nope! The denominators don't match. We need a common denominator. So next we take both denominators and multiply them. Next, take each numerator and multiply it by the denominator of the other term.

So, we multiply 78 by 8, and get 624, then we multiply 10 by 8 and get 80.

78/10 times 8

Now for the second term. You multiply 7 by 10, and get 70, then multiply 10 by 8 and get 80.

7/8 times 10

We now have a new problem, that looks like this:

624
80
+
70
80

Step 2

Since our denominators match, we can add the numerators.

624 + 70 = 694

That gives us the sum, which is

694
80

Step 3

Now, do we need to simplify this fraction?

First, we attempt to divide it by 2...

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

694
80
÷ 2 =
347
40

Now, try the same number again.

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

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

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

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

Nope. Try the next prime number, 13...

Nope. Try the next prime number, 17...

Nope. Try the next prime number, 19...

Nope. Try the next prime number, 23...

Nope. Try the next prime number, 29...

Nope. Try the next prime number, 31...

Nope. Try the next prime number, 37...

Nope. Try the next prime number, 41...

No good. 41 is larger than 40. So we're done reducing.

Congratulations! Here's your final answer to 78/10 + 7/8

78
10
+
7
8
=
347
40
© 2014 Randy Tayler