math help

What is 7/16 + 6/9?

What is 7/16 + 6/9?

This is how we add

7
16
 +
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 16 by 9 and get 144.

7/16 times 9

Do the same for the second term. We multiply 6 by 16, and get 96, then multiply 16 by 9 and get 144.

6/9 times 16

The problem now has new fractions to add:

63
144
 +
96
144

Step 2

Since our denominators match, we can add the numerators.

63 + 96 = 159

The sum we get is

159
144

Step 3

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

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

No good. So next you try the next prime number, which is 3...

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

159
144
 ÷ 3 =
53
48

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 5...

No good. So next you try the next prime number, which is 7...

No good. So next you try the next prime number, which is 11...

No good. So next you try the next prime number, which is 13...

No good. So next you try the next prime number, which is 17...

No good. So next you try the next prime number, which is 19...

No good. So next you try the next prime number, which is 23...

No good. So next you try the next prime number, which is 29...

No good. So next you try the next prime number, which is 31...

No good. So next you try the next prime number, which is 37...

No good. So next you try the next prime number, which is 41...

No good. So next you try the next prime number, which is 43...

No good. So next you try the next prime number, which is 47...

No good. So next you try the next prime number, which is 53...

No good. 53 is larger than 48. So we're done reducing.

And we're done! Here's the final answer to 7/16 + 6/9

7
16
 +
6
9
 =
53
48
© 2014 Randy Tayler

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