math help

What is 78/10 + 8/9?

What is 78/10 + 8/9?

Here's how to add

78
10
+
8
9

Step 1

We still have different denominators (bottom numbers), though, so we need to get a common denominator. This will make the bottom numbers match. Multiply the denominators together first. Now, multiply each numerator by the other term's denominator.

Now we multiply 78 by 9, and get 702, then we multiply 10 by 9 and get 90.

78/10 times 9

Now for the second term. You multiply 8 by 10, and get 80, then multiply 10 by 9 and get 90.

8/9 times 10

This gives us a new problem that looks like so:

702
90
+
80
90

Step 2

Since our denominators match, we can add the numerators.

702 + 80 = 782

That gives us an answer of

782
90

Step 3

Can this fraction be reduced?

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

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

782
90
÷ 2 =
391
45

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 3...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

Nope! So now we try the next greatest prime number, 11...

Nope! So now we try the next greatest prime number, 13...

Nope! So now we try the next greatest prime number, 17...

Nope! So now we try the next greatest prime number, 19...

Nope! So now we try the next greatest prime number, 23...

Nope! So now we try the next greatest prime number, 29...

Nope! So now we try the next greatest prime number, 31...

Nope! So now we try the next greatest prime number, 37...

Nope! So now we try the next greatest prime number, 41...

Nope! So now we try the next greatest prime number, 43...

Nope! So now we try the next greatest prime number, 47...

No good. 47 is larger than 45. So we're done reducing.

There you have it! Here's the final answer to 78/10 + 8/9

78
10
+
8
9
=
391
45
© 2014 Randy Tayler