math help

What is 4/40 + 10/12?

What is 4/40 + 10/12?

This is how we add

4
40
 +
10
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 4 by 12, and get 48, then we multiply 40 by 12 and get 480.

4/40 times 12

Do the same for the second term. We multiply 10 by 40, and get 400, then multiply 40 by 12 and get 480.

10/12 times 40

The problem now has new fractions to add:

48
480
 +
400
480

Step 2

Since our denominators match, we can add the numerators.

48 + 400 = 448

This yields the answer

448
480

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:

448
480
 ÷ 2 =
224
240

Let's try dividing by that again...

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

224
240
 ÷ 2 =
112
120

Let's try dividing by that again...

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

112
120
 ÷ 2 =
56
60

Let's try dividing by that again...

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

56
60
 ÷ 2 =
28
30

Let's try dividing by that again...

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

28
30
 ÷ 2 =
14
15

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...

No good. 17 is larger than 14. So we're done reducing.

There you have it! Here's the final answer to 4/40 + 10/12

4
40
 +
10
12
 =
14
15
© 2014 Randy Tayler

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