math help

What is 36/4 + 4/6?

What is 36/4 + 4/6?

Let's add

36
4
 +
4
6

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 36 by 6, and get 216, then we multiply 4 by 6 and get 24.

36/4 times 6

Do the same for the second term. We multiply 4 by 4, and get 16, then multiply 4 by 6 and get 24.

4/6 times 4

The problem now has new fractions to add:

216
24
 +
16
24

Step 2

Since our denominators match, we can add the numerators.

216 + 16 = 232

This yields the answer

232
24

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:

232
24
 ÷ 2 =
116
12

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

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

116
12
 ÷ 2 =
58
6

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

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

58
6
 ÷ 2 =
29
3

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...

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

No good. 5 is larger than 3. So we're done reducing.

And we're done! Here's the final answer to 36/4 + 4/6

36
4
 +
4
6
 =
29
3
© 2014 Randy Tayler

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