Okay, let's do this. In order to add or subtract fractions, you have to find the least common denominator. First of all, let's convert these mixed numbers to fractions. To convert:

If the mixed number is represented symbolically, it would look something like I and n/d, where I is the integer (in 4 and 1/2, I is the 4), n is the numerator (in 4 and 1/2, n is the 1) and d is the denominator (in 4 and 1/2, d is the 2).

To convert it to a fraction, you multiply I by d and add n, or (I * d) + n = the new numerator. The denominator stays the same. So, 4 and 1/2 becomes:

(4 * 2) + 1 = 9, and the fraction becomes 9/2.

If you perform the same thing on 8 and 1/5, you get (8 * 5) + 1 = 41, and the fraction becomes 41/5.

So your two new fractions are 9/2 and 41/5

To find the least common denominator, multiply each fraction by the denominator of the other fraction:

9/2 * 5/5 = 45/10

41/5 * 2/2 = 82/10

Once both denominators are the same (10, in this case), you can simply add or subtract the numerators:

45/10 - 82/10 = -37/10

The result is negative because 8 and 1/5 is greater than 4 and 1/2.

You could leave your answer at -37/10 if you wanted to, or you could convert it back to mixed numbers. To find the integer of an improper fraction, you find how many times the denominator goes into the numerator. -37 can be divided by 10 three full times before you have fractions, so:

-37/10 = -3 remainder 7

Your integer will be -3, your numerator will be 7, and your denominator will be 10: -3 and 7/10.

So, 4 1/2 - 8 1/5 = -3 7/10.

If the mixed number is represented symbolically, it would look something like I and n/d, where I is the integer (in 4 and 1/2, I is the 4), n is the numerator (in 4 and 1/2, n is the 1) and d is the denominator (in 4 and 1/2, d is the 2).

To convert it to a fraction, you multiply I by d and add n, or (I * d) + n = the new numerator. The denominator stays the same. So, 4 and 1/2 becomes:

(4 * 2) + 1 = 9, and the fraction becomes 9/2.

If you perform the same thing on 8 and 1/5, you get (8 * 5) + 1 = 41, and the fraction becomes 41/5.

So your two new fractions are 9/2 and 41/5

To find the least common denominator, multiply each fraction by the denominator of the other fraction:

9/2 * 5/5 = 45/10

41/5 * 2/2 = 82/10

Once both denominators are the same (10, in this case), you can simply add or subtract the numerators:

45/10 - 82/10 = -37/10

The result is negative because 8 and 1/5 is greater than 4 and 1/2.

You could leave your answer at -37/10 if you wanted to, or you could convert it back to mixed numbers. To find the integer of an improper fraction, you find how many times the denominator goes into the numerator. -37 can be divided by 10 three full times before you have fractions, so:

-37/10 = -3 remainder 7

Your integer will be -3, your numerator will be 7, and your denominator will be 10: -3 and 7/10.

So, 4 1/2 - 8 1/5 = -3 7/10.