math help

What is 24/26 + 10/12?

What is 24/26 + 10/12?

This is how you add

24
26
 +
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 24 by 12, and get 288, then we multiply 26 by 12 and get 312.

24/26 times 12

Do the same for the second term. We multiply 10 by 26, and get 260, then multiply 26 by 12 and get 312.

10/12 times 26

So now our fractions look like this:

288
312
 +
260
312

Step 2

Since our denominators match, we can add the numerators.

288 + 260 = 548

So the answer is:

548
312

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:

548
312
 ÷ 2 =
274
156

Let's try dividing by that again...

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

274
156
 ÷ 2 =
137
78

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...

Nope! So now we try the next greatest prime number, 53...

Nope! So now we try the next greatest prime number, 59...

Nope! So now we try the next greatest prime number, 61...

Nope! So now we try the next greatest prime number, 67...

Nope! So now we try the next greatest prime number, 71...

Nope! So now we try the next greatest prime number, 73...

Nope! So now we try the next greatest prime number, 79...

No good. 79 is larger than 78. So we're done reducing.

There you have it! Here's the final answer to 24/26 + 10/12

24
26
 +
10
12
 =
137
78
© 2014 Randy Tayler

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