math help

What is 4/10 + 10/12?

What is 4/10 + 10/12?

Let's add

4
10
+
10
12

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 4 by 12, and get 48, then we multiply 10 by 12 and get 120.

4/10 times 12

Do the same for the second term. We multiply 10 by 10, and get 100, then multiply 10 by 12 and get 120.

10/12 times 10

So now our fractions look like this:

48
120
+
100
120

Step 2

Since our denominators match, we can add the numerators.

48 + 100 = 148

Now we have an answer.

148
120

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...

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

148
120
÷ 2 =
74
60

Let's try dividing by that again...

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

74
60
÷ 2 =
37
30

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 3...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

Nope! So now we try the next greatest prime number, 11...

Nope! So now we try the next greatest prime number, 13...

Nope! So now we try the next greatest prime number, 17...

Nope! So now we try the next greatest prime number, 19...

Nope! So now we try the next greatest prime number, 23...

Nope! So now we try the next greatest prime number, 29...

Nope! So now we try the next greatest prime number, 31...

No good. 31 is larger than 30. So we're done reducing.

There you have it! Here's the final answer to 4/10 + 10/12

4
10
+
10
12
=
37
30
© 2014 Randy Tayler