math help

What is 7/10 + 9/12?

What is 7/10 + 9/12?

This is how we add

7
10
 +
9
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 7 by 12, and get 84, then we multiply 10 by 12 and get 120.

7/10 times 12

Do the same for the second term. We multiply 9 by 10, and get 90, then multiply 10 by 12 and get 120.

9/12 times 10

The problem now has new fractions to add:

84
120
 +
90
120

Step 2

Since our denominators match, we can add the numerators.

84 + 90 = 174

The sum we get is

174
120

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:

174
120
 ÷ 2 =
87
60

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:

87
60
 ÷ 3 =
29
20

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. 23 is larger than 20. So we're done reducing.

And we're done! Here's the final answer to 7/10 + 9/12

7
10
 +
9
12
 =
29
20
© 2014 Randy Tayler

9/12 + 1/2
9/12 - 1/2
9/12 + 1/3
9/12 - 1/3
9/12 + 2/3
9/12 - 2/3
9/12 + 1/4
9/12 - 1/4
9/12 + 2/4
9/12 - 2/4
9/12 + 3/4
9/12 - 3/4
9/12 + 1/5
9/12 - 1/5
9/12 + 2/5
9/12 - 2/5
9/12 + 3/5
9/12 - 3/5
9/12 + 4/5
9/12 - 4/5
9/12 + 1/6
9/12 - 1/6
9/12 + 2/6
9/12 - 2/6
9/12 + 3/6
9/12 - 3/6
9/12 + 4/6
9/12 - 4/6
9/12 + 5/6
9/12 - 5/6
9/12 + 1/7
9/12 - 1/7
9/12 + 2/7
9/12 - 2/7
9/12 + 3/7
9/12 - 3/7
9/12 + 4/7
9/12 - 4/7
9/12 + 5/7
9/12 - 5/7
9/12 + 6/7
9/12 - 6/7
9/12 + 1/8
9/12 - 1/8
9/12 + 2/8
9/12 - 2/8
9/12 + 3/8
9/12 - 3/8
9/12 + 4/8
9/12 - 4/8
9/12 + 5/8
9/12 - 5/8
9/12 + 6/8
9/12 - 6/8
9/12 + 7/8
9/12 - 7/8
9/12 + 1/9
9/12 - 1/9
9/12 + 2/9
9/12 - 2/9
9/12 + 3/9
9/12 - 3/9
9/12 + 4/9
9/12 - 4/9
9/12 + 5/9
9/12 - 5/9
9/12 + 6/9
9/12 - 6/9
9/12 + 7/9
9/12 - 7/9
9/12 + 8/9
9/12 - 8/9
9/12 + 1/10
9/12 - 1/10
9/12 + 2/10
9/12 - 2/10
9/12 + 3/10
9/12 - 3/10
9/12 + 4/10
9/12 - 4/10
9/12 + 5/10
9/12 - 5/10
9/12 + 6/10
9/12 - 6/10
9/12 + 7/10
9/12 - 7/10
9/12 + 8/10
9/12 - 8/10
9/12 + 9/10
9/12 - 9/10
9/12 + 1/11
9/12 - 1/11
9/12 + 2/11
9/12 - 2/11
9/12 + 3/11
9/12 - 3/11
9/12 + 4/11
9/12 - 4/11
9/12 + 5/11
9/12 - 5/11
9/12 + 6/11
9/12 - 6/11
9/12 + 7/11
9/12 - 7/11
9/12 + 8/11
9/12 - 8/11
9/12 + 9/11
9/12 - 9/11
9/12 + 10/11
9/12 - 10/11
9/12 + 1/12
9/12 - 1/12
9/12 + 2/12
9/12 - 2/12
9/12 + 3/12
9/12 - 3/12
9/12 + 4/12
9/12 - 4/12
9/12 + 5/12
9/12 - 5/12
9/12 + 6/12
9/12 - 6/12
9/12 + 7/12
9/12 - 7/12
9/12 + 8/12
9/12 - 8/12
9/12 + 9/12
9/12 - 9/12
9/12 + 10/12
9/12 - 10/12
9/12 + 11/12
9/12 - 11/12