Using reasoning to solve problems - HiSET

One yard is equivalent to 3 feet, so feet can be converted to yards by dividing by the conversion factor 3:

Also, one yard is equal to 36 inches, so 18 inches can be converted to yards by dividing by the conversion factor 36;

Add these quantities:

Rewriting with the least common denominator, which is 6:

,

the correct choice.

One gallon is equivalent to 4 quarts, so 16 gallons can be converted to quarts by multiplying by conversion factor 4:

One quart is equivalent to 2 pints, so pints can be converted to quarts by dividing by conversion factor 2:

Added together:

,

the correct response.

One gallon is equivalent to 4 quarts, so gallons can be converted to quarts by multiplying by conversion factor 4:

One quart is equivalent to 2 pints, so 10 pints can be converted to quarts by dividing by conversion factor 2:

Added together:

,

the correct response.

One meter is equivalent to 100 centimeters, so meters can be converted to centimeters by multiplying by conversion factor 100:

One centimeter is equivalent to 10 millimeters, so 50 millimeters can be converted to centimeters by dividing by conversion factor 10:

Add these quantities:

,

the correct response.

One yard is equivalent to 3 feet, so 2 feet can be converted to yards by dividing by the conversion factor 3:

Also, one yard is equal to 36 inches, so inches can be converted to yards by dividing by the conversion factor 36;

Add these quantities:

Rewriting with the least common denominator, which is 36:

,

the correct choice.

One gram is equivalent to 1,000 milligrams, so milligrams can be converted to grams by dividing by conversion factor 1,000:

One gram is also equivalent to 100 centigrams, so centigrams can be converted to grams by dividing by conversion factor 100:

Add:

Rewrite in terms of lowest common denominator 1,000:

,

the correct response.

The measure of a rectangular plot of land is equal to the product of its dimensions, so the given plot has area

One square mile is equivalent to 640 acres, so multiply this by conversion factor 640:

,

the correct response.

One square mile is equivalent to 640 acres. Therefore, the area of the plot, 72 acres, can be converted to square miles by dividing by conversion factor 640:

If we let and be the north-south and east-west lengths in miles of the rectangular land plot, respectively, then

Substitute for :

Solve for by multiplying both sides by 4:

The east-west length of the plot is mile.

One gallon is equivalent to 4 quarts.

One quart is equivalent to 2 pints.

One pint is equivalent to 2 cups.

Therefore, one gallon is equivalent to cups.

Pouring out one cup leaves 15 cups, the correct response.

528 yards, the sidelength of the square plot, can be converted to square miles as follows:

1,760 yards are equivalent to one mile. Therefore, 528 can be divided by conversion factor 1,760:

The area of the plot is equal to the square of this, or

One square mile is equivalent to 640 acres, so multiply by conversion factor 640:

,

the correct response.

This problem can be solved using a proportion statement.

One meter is equal to 100 centimeters, which in turn is equal to 39.37 inches. Letting be the centimeter equivalent of 30 inches, the proportion statement that relates centimeters and inches can be written

Multiply both sides by 30:

A square plot of land has as its area the square of the length of a side, so the land in question has area

square miles.

One square mile is equal to 640 acres, so multiply this by the conversion factor 640:

One gallon is equivalent to 4 quarts, so 16 gallons can be converted to quarts by multiplying by conversion factor 4:

One quart is equivalent to 2 pints, so pints can be converted to quarts by dividing by conversion factor 2:

Added together:

,

the correct response.

One gallon is equivalent to 4 quarts, so gallons can be converted to quarts by multiplying by conversion factor 4:

One quart is equivalent to 2 pints, so 10 pints can be converted to quarts by dividing by conversion factor 2:

Added together:

,

the correct response.

One meter is equivalent to 100 centimeters, so meters can be converted to centimeters by multiplying by conversion factor 100:

One centimeter is equivalent to 10 millimeters, so 50 millimeters can be converted to centimeters by dividing by conversion factor 10:

Add these quantities:

,

the correct response.

One meter is equivalent to 100 centimeters, so 2 meters can be converted to centimeters by multiplying by conversion factor 100:

One centimeter is equivalent to 10 millimeters, so millimeters can be converted to centimeters by dividing by conversion factor 10:

Add these quantities:

,

the correct answer.

One yard is equivalent to 3 feet, so feet can be converted to yards by dividing by the conversion factor 3:

Also, one yard is equal to 36 inches, so 18 inches can be converted to yards by dividing by the conversion factor 36;

Add these quantities:

Rewriting with the least common denominator, which is 6:

,

the correct choice.

One yard is equivalent to 3 feet, so 2 feet can be converted to yards by dividing by the conversion factor 3:

Also, one yard is equal to 36 inches, so inches can be converted to yards by dividing by the conversion factor 36;

Add these quantities:

Rewriting with the least common denominator, which is 36:

,

the correct choice.

One gram is equivalent to 1,000 milligrams, so milligrams can be converted to grams by dividing by conversion factor 1,000:

One gram is also equivalent to 100 centigrams, so centigrams can be converted to grams by dividing by conversion factor 100:

Add:

Rewrite in terms of lowest common denominator 1,000:

,

the correct response.