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 .

The distributive property of multiplication over addition is the idea that, if a number is multiplied by a sum, the result will be the same as if the products of that number and each individual addend are added. The diagram that demonstrates this is 

.

Addition and multiplication are both associative, which means that a sum or product of three numbers will result in the same value regardless of which two are added or multiplied first. This is demonstrated in multiplication by the diagram

.

According to the transitive property of equality, if two numbers are equal to the same third number, they are equal to each other. This is demonstrated by this diagram:

If  and , then 

According to the symmetric property of equality, if one number is equal to another, the second is equal to the first. This is demonstrated by the diagram

If  then 

0 is called the additive identity, since it can be added to any number to yield, as a sum, the latter number. This property is demonstrated in the diagram

If  is the additive inverse of , then 

, or, equivalently,

Substituting,

.