math help

What is 78/10 + 11/12?

What is 78/10 + 11/12?

This is how to add

78
10
 +
11
12

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

78/10 times 12

Now for the second term. You multiply 11 by 10, and get 110, then multiply 10 by 12 and get 120.

11/12 times 10

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

936
120
 +
110
120

Step 2

Since our denominators match, we can add the numerators.

936 + 110 = 1046

That gives us the sum, which is

1046
120

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:

1046
120
 ÷ 2 =
523
60

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...

Nope! So now we try the next greatest prime number, 53...

Nope! So now we try the next greatest prime number, 59...

Nope! So now we try the next greatest prime number, 61...

No good. 61 is larger than 60. So we're done reducing.

There you have it! Here's the final answer to 78/10 + 11/12

78
10
 +
11
12
 =
523
60
© 2014 Randy Tayler

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