math help

What is 48/30 + 7/9?

What is 48/30 + 7/9?

This is how we add

48
30
+
7
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 48 by 9, and get 432, then we multiply 30 by 9 and get 270.

48/30 times 9

Do the same for the second term. We multiply 7 by 30, and get 210, then multiply 30 by 9 and get 270.

7/9 times 30

The problem now has new fractions to add:

432
270
+
210
270

Step 2

Since our denominators match, we can add the numerators.

432 + 210 = 642

The sum we get is

642
270

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:

642
270
÷ 2 =
321
135

Now, try the same number again.

Nope. Try the next prime number, 3...

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

321
135
÷ 3 =
107
45

Now, try the same number again.

Nope. Try the next prime number, 5...

Nope. Try the next prime number, 7...

Nope. Try the next prime number, 11...

Nope. Try the next prime number, 13...

Nope. Try the next prime number, 17...

Nope. Try the next prime number, 19...

Nope. Try the next prime number, 23...

Nope. Try the next prime number, 29...

Nope. Try the next prime number, 31...

Nope. Try the next prime number, 37...

Nope. Try the next prime number, 41...

Nope. Try the next prime number, 43...

Nope. Try the next prime number, 47...

No good. 47 is larger than 45. So we're done reducing.

Congratulations! Here's your final answer to 48/30 + 7/9

48
30
+
7
9
=
107
45
© 2014 Randy Tayler