math help

What is 4/52 + 6/10?

What is 4/52 + 6/10?

This is how you add

4
52
 +
6
10

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 10, and get 40, then we multiply 52 by 10 and get 520.

4/52 times 10

Do the same for the second term. We multiply 6 by 52, and get 312, then multiply 52 by 10 and get 520.

6/10 times 52

So now our fractions look like this:

40
520
 +
312
520

Step 2

Since our denominators match, we can add the numerators.

40 + 312 = 352

So the answer is:

352
520

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:

352
520
 ÷ 2 =
176
260

Let's try dividing by that again...

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

176
260
 ÷ 2 =
88
130

Let's try dividing by that again...

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

88
130
 ÷ 2 =
44
65

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...

Nope! So now we try the next greatest prime number, 37...

Nope! So now we try the next greatest prime number, 41...

Nope! So now we try the next greatest prime number, 43...

Nope! So now we try the next greatest prime number, 47...

No good. 47 is larger than 44. So we're done reducing.

There you have it! Here's the final answer to 4/52 + 6/10

4
52
 +
6
10
 =
44
65
© 2014 Randy Tayler

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