Recall that the exponent of the denominator is sutracted from the exponent of the numerator. 

Therefore Quantity A is equivalent to x^5–y, and because we would then be comparing an arithmetic operation to a geometric operation, it does not matter whether y is a multiple of 5.  The two quantities cannot be compared.

To begin, notice that using your calculator, you can find:

Now, the closest even multiple of  that is less than  is .  Therefore, you know that your number is:

This is the same as:

, or simply, .  This is your mixed fraction.

Although there are many ways to convert improper fractions into mixed fractions, the easiest way is to use your calculator to your advantage.  Begin by dividing  by .  This gives you . Therefore, you can eliminate all the options that have do not have  for their first portion. Next, multiply  by the denominator (), and get .  This means that you have  and , or .  Thus, your answer is .

Though there are several ways you could solve this, let's convert the improper fraction into a mixed one so we can compare them. Start by dividing  by .  This gives you  

Now, since we know that the two numbers have the same whole-number value, we need to compare their decimal portions. Compare  to . The latter is indeed   Therefore, the two values are equal.

To find the improper fraction value, we must effectively add together 71 and ⁵/₇. To do this, we will give 71 a denominator of 7; therefore, we are transforming ⁷¹/₁ to ^x/₇.  The shortest way to do this is to multiply by ⁷/₇ (which really is 1); therefore, 71 = 71 * (⁷/₇) = ⁴⁹⁷/₇.

Now add them: ^{(497 + 5)}/₇ = ⁵⁰²/₇

To find an improper fraction, you need to multiply the whole number that you have by the denominator of the associated fraction.  For our problem, this means that you will multiply  by , getting .  Next, you add this to the numerator of your fraction, giving you , or .  Finally, you place this over your original denominator, giving you: 

To find an improper fraction, you need to multiply the whole number that you have by the denominator of the associated fraction.  For our problem, this means that you will multiply  by , getting .  Next, you add this to the numerator of your fraction, giving you , or .  Finally, you place this over your original denominator, giving you: 

The arithmetic mean of a set is defined as the sum of terms in the set divided by the number of terms of a set. Therefore, the mean for this problem can be found as:

There are  slips of paper that have a number divisible by , which are . 

The probability of one being drawn is . Once that slip is drawn, the probability of drawing a number divisible by  becomes , and on the third draw it is .

For this sequence of events to happen, the probability is the product of the three separate probabilities:

Both of these sundae options are dealing with combinations, i.e. the order the scoops are chosen does not matter, and so the amount of possible combos is given by the formula:

Where  is the total number of options and  is the size of the combination created.

For the Triple Trouble, the total amount of possible sundaes is:

And for the Fearsome Four: