math help

What is 7/20 + 6/9?

What is 7/20 + 6/9?

Here's how to add

7
20
 +
6
9

Step 1

Of course, you can't add two fractions if the denominators (bottom numbers) don't match. To get a common denominator, multiply the denominators together. Then we fix the numerators by multiplying each one by their other term's denominator.

Now you multiply 7 by 9, and get 63, then we multiply 20 by 9 and get 180.

7/20 times 9

Do the same for the second term. We multiply 6 by 20, and get 120, then multiply 20 by 9 and get 180.

6/9 times 20

The problem now has new fractions to add:

63
180
 +
120
180

Step 2

Since our denominators match, we can add the numerators.

63 + 120 = 183

This yields the answer

183
180

Step 3

The last step is to reduce the fraction if we can.

To find out, we try dividing it by 2...

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:

183
180
 ÷ 3 =
61
60

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...

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 7/20 + 6/9

7
20
 +
6
9
 =
61
60
© 2014 Randy Tayler

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