math help

What is 20/64 + 6/9?

What is 20/64 + 6/9?

Let's add

20
64
 +
6
9

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 20 by 9, and get 180, then we multiply 64 by 9 and get 576.

20/64 times 9

Now for the second term. You multiply 6 by 64, and get 384, then multiply 64 by 9 and get 576.

6/9 times 64

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

180
576
 +
384
576

Step 2

Since our denominators match, we can add the numerators.

180 + 384 = 564

Answer:

564
576

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:

564
576
 ÷ 2 =
282
288

Let's try dividing by that again...

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

282
288
 ÷ 2 =
141
144

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:

141
144
 ÷ 3 =
47
48

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...

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...

No good. 53 is larger than 47. So we're done reducing.

There you have it! Here's the final answer to 20/64 + 6/9

20
64
 +
6
9
 =
47
48
© 2014 Randy Tayler

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