math help

What is 1/15 + 10/12?

What is 1/15 + 10/12?

This is how we add

1
15
 +
10
12

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 1 by 12, and get 12, then we multiply 15 by 12 and get 180.

1/15 times 12

Do the same for the second term. We multiply 10 by 15, and get 150, then multiply 15 by 12 and get 180.

10/12 times 15

The problem now has new fractions to add:

12
180
 +
150
180

Step 2

Since our denominators match, we can add the numerators.

12 + 150 = 162

The sum we get is

162
180

Step 3

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

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

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

162
180
 ÷ 2 =
81
90

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 3...

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

81
90
 ÷ 3 =
27
30

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

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

27
30
 ÷ 3 =
9
10

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. 11 is larger than 9. So we're done reducing.

And we're done! Here's the final answer to 1/15 + 10/12

1
15
 +
10
12
 =
9
10
© 2014 Randy Tayler

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