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What is 100/72 - 2/6?

What is 100/72 - 2/6?

Here's how to subtract 2/6 from 100/72:

100
72
 −
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 100 by 6, and get 600.

Then we multiply 2 by 72, and get 144.

Next we give both terms new denominators -- 72 × 6 = 432.

So now our fractions look like this:

600
432
 −
144
432

Step 2

Since our denominators match, we can subtract the numerators.

600 − 144 = 456

So the answer is:

456
432

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:

456
432
 ÷ 2 =
228
216

Let's try dividing by 2 again...

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

228
216
 ÷ 2 =
114
108

Let's try dividing by 2 again...

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

114
108
 ÷ 2 =
57
54

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:

57
54
 ÷ 3 =
19
18

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...

No good. 19 is larger than 18. So we're done reducing.

There you have it! The final answer is:
100
72
 −
2
6
 =
19
18

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