How to make non-geometric comparisons

a) The square root of is , because .

b) of is , because .

c) The average of and is , because .

Therefore (b) and (c) are equal, and they are both smaller than (a).

To find a percentage of the number, multiply it by the decimal version of the percent, or the percent divided by .

Therefore, percent of is equal to , or

Multiply the fractions by the integers in order to compare the expressions:

a)

b)

c)

It is now clear that (b) is smaller than (a), which is smaller than (c).

Follow the order of operations when simplifying these expressions. First parantheses, then multiplication, and finally addition:

a)

b)

c)

Therefore (b) is less than (c), which is less than (a).

Calculate the expressions to compare the values:

a) of

b) percent of

c)

Now it is clear that (a) and (b) are equal, and (c) is greater than both of them.

You don't need to calculate any square roots to solve this problem! Just remember the following property:

Following this property, (a) and (b) are equal:

This also means that the following is true:

And therefore:

(c) is just a simplified version of (a) and (b)

Calculate each expression in order to compare them:

a) of

b) of

c) of

(b) and (c) are equal, and (a) is greater than both.

a)

This expression is already simplified.

b)

This expression simplifies to .

c)

This expression also simplifies to .

Clearly (b) and (c) are equal, but (a) is smaller because it has a smaller numerator.

is ten added to the square of ten - that is,

Evaluate this according to the order of operations by squaring, then by adding.

Evaluate the other two expressions using the same order:

is twenty added to the square of nine, so

is thirty added to the square of eight, so

, so the only correct statement of the four is .

Multiply each fraction by the number to find each value:

a) of

b) of

c) of

Therefore (a) is less than (c), which is less than (b).