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What is 78/92 - 6/9?

What is 78/92 - 6/9?

Here's how to subtract 6/9 from 78/92:

78
92
6
9

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 78 by 9, and get 702.

Then we multiply 6 by 92, and get 552.

Next we give both terms new denominators -- 92 × 9 = 828.

So now our fractions look like this:

702
828
552
828

Step 2

Since our denominators match, we can subtract the numerators.

702 − 552 = 150

So the answer is:

150
828

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:

150
828
÷ 2 =
75
414

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:

75
414
÷ 3 =
25
138

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...

No good. 29 is larger than 25. So we're done reducing.

There you have it! The final answer is:
78
92
6
9
=
25
138