The one-hundredths place is the second place to the right of the decimal point; therefore, three one-hundredths is equal to 0.03. One fourth can be converted to decimal form as follows:

,

which is twenty-five one-hundredths, or 0.25. Subtract:

,

or twenty-two one-hundredths.

We can find each in terms of .

In ascending order, the numbers are:

The correct choice is  .

The expression is equal to , which is calculated as follows:

,

or seventeen twenty-eighths.

. As the product of integers,  must be an integer. 

, making  the sum of integers, and, consequently, an integer.

, making  the sum of integers, and, consequently, an integer.

, making  the difference of integers, and, consequently, an integer.

We demonstrate that need not be an integer through a counterexample. Let .

 and , so the conditions of the problem are met. However,

, which is not an integer. This makes  the correct response.

In the absence of grouping symbols, all multiplications are performed before any of the subtractions. Therefore, the first two operations performed are the multiplications. The three remaining operations, all subtractions, are performed right to left, so the next operation - the third one - to be performed is the leftmost subtraction.

In the absence of grouping symbols, additions and subtractions are performed with precedence moving from left to right. Therefore, the five operations, each an addition or a subtraction, are performed right to left, and the third operation performed is the middle subtraction.

Since there are no grouping symbols in any of the expressions, the order of operations dictates that the multiplication and division must be worked before the addition in each. The operations must be worked from left to right. Only in expression (III) does the multiplication occur before the division when reafing left to right, so this is the only expession evaluated by multiplying first.

In the absence of grouping symbols, additions and subtractions are performed from left to right. Only the expression in (I) has an addition as its leftmost operation, so this is the only expression that is evaluated by adding first.

In the absence of grouping symbols, multiplications and divisions are performed with precedence moving from left to right. Therefore, the five operations, each a multiplication or a division, are performed left to right, and the second operation performed is the leftmost multiplication.

The sequence of numbers in the upper left entries of the boxes is simply the sequence of natural numbers. The upper left number in the twelfth box will be .

The sequence of numbers in the upper right entries of the boxes is the sequence of powers of 2, beginning with . The upper right number in the twelfth box will be .

The sequence of numbers in the lower left entries of the boxes is the Fibonacci sequence, whose terms after the second are each the sum of the preceding two. To get the twelfth term requires a little work, but we can do it as follows:

The entry in the lower right is the sum of the other three entries, so the lower right entry in the twelfth box will be

.

The correct choice is that .