math help

What is 7/49 + 3/5?

What is 7/49 + 3/5?

Let's add

7
49
+
3
5

Step 1

We can't add two fractions with different denominators (the bottom number). So you need to get a common denominator - both bottom numbers need to match. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 7 by 5, and get 35, then we multiply 49 by 5 and get 245.

7/49 times 5

Do the same for the second term. We multiply 3 by 49, and get 147, then multiply 49 by 5 and get 245.

3/5 times 49

So now our fractions look like this:

35
245
+
147
245

Step 2

Since our denominators match, we can add the numerators.

35 + 147 = 182

So the answer is:

182
245

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

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

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

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

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

Are both the numerator and the denominator evenly divisible by 7? Yes! So we reduce it:

182
245
÷ 7 =
26
35

Now, try the same number again.

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...

No good. 29 is larger than 26. So we're done reducing.

Congratulations! Here's your final answer to 7/49 + 3/5

7
49
+
3
5
=
26
35
© 2014 Randy Tayler