math help

What is 70/51 - 2/6?

What is 70/51 - 2/6?

Here's how to subtract 2/6 from 70/51:

70
51
 −
2
6

Step 1

We can't subtract two fractions with different denominators. So you need to get a common denominator. 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 70 by 6, and get 420.

Then we multiply 2 by 51, and get 102.

Next we give both terms new denominators -- 51 × 6 = 306.

So now our fractions look like this:

420
306
 −
102
306

Step 2

Since our denominators match, we can subtract the numerators.

420 − 102 = 318

So the answer is:

318
306

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:

318
306
 ÷ 2 =
159
153

Let's try dividing by 2 again...

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

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

159
153
 ÷ 3 =
53
51

Let's try dividing by 3 again...

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...

No good. 53 is larger than 51. So we're done reducing.

There you have it! The final answer is:
70
51
 −
2
6
 =
53
51

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