math help

What is 8/9 + 10/12?

What is 8/9 + 10/12?

Here's how we add

8
9
 +
10
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 8 by 12, and get 96, then we multiply 9 by 12 and get 108.

8/9 times 12

Now for the second term. You multiply 10 by 9, and get 90, then multiply 9 by 12 and get 108.

10/12 times 9

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

96
108
 +
90
108

Step 2

Since our denominators match, we can add the numerators.

96 + 90 = 186

That gives us the sum, which is

186
108

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:

186
108
 ÷ 2 =
93
54

Let's try dividing by that again...

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

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

93
54
 ÷ 3 =
31
18

Let's try dividing by that again...

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...

No good. 19 is larger than 18. So we're done reducing.

There you have it! Here's the final answer to 8/9 + 10/12

8
9
 +
10
12
 =
31
18
© 2014 Randy Tayler

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