math help

What is 78/10 - 4/6?

What is 78/10 - 4/6?

Here's how to subtract 4/6 from 78/10:

78
10
 −
4
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 78 by 6, and get 468.

Then we multiply 4 by 10, and get 40.

Next we give both terms new denominators -- 10 × 6 = 60.

So now our fractions look like this:

468
60
 −
40
60

Step 2

Since our denominators match, we can subtract the numerators.

468 − 40 = 428

So the answer is:

428
60

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:

428
60
 ÷ 2 =
214
30

Let's try dividing by 2 again...

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

214
30
 ÷ 2 =
107
15

Let's try dividing by 2 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...

No good. 17 is larger than 15. So we're done reducing.

There you have it! The final answer is:
78
10
 −
4
6
 =
107
15

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