(2) The product or quotient of a negative number and a positive number is a negative number.

(3) The product or quotient of two negative numbers is a positive number.

(4) Exponents with a negative number in the base will result in a negative number if the number in the exponent is odd but a positive number if the exponent is even.

*Product: the name for the number or answer obtained from multiplication

*Quotient: the name for the number or answer obtained from division

Multiplication

*I made a mistake around the 4:18 mark at the end of the question in the 3 x 2 and 3 x 3 digit multiplication video. I mistook a 0 for an 8 when adding, which messed up the final answer. The correct final answer is 133,722.

To multiply with negative numbers, do the multiplication as you would if both numbers were positive and consider the rules for multiplication with negative numbers further up on this page to determine whether your final answer (product) is negative or positive.

You see in the video that an answer to a division problem that results in a number with a decimal can be expressed in two ways. Consider the following division (from video):

The answer can be expressed as 54 R4 or 54 ⅓.

And as with multiplication, if you are divided numbers that have decimals, an easy way to do this with the above algorithm is to do the division without the decimal points, and then just put the decimal point "where it makes sense".

So, for the above question, if we were doing 65.2 divided by 12, 54 wouldn't make sense but 5.4 would.

The square of a number is the number multiplied by itself. A number “squared” is simply the number raised to the exponent 2.

Any number can be squared (whole numbers, fractions or decimals, negative numbers, etc.). The “perfect squares”, however, are the squares of the positive integers:

The square root can be thought of as the opposite of the square. The square root symbol (the checkmark-like symbol) seen below is sometimes called the radical.

If the square is 144, the square root is 12. The square root is 12 because 12 multiplied by itself would give you the square, 144. The following shows the square roots of the perfect squares.

You should have the square roots of the perfect squares memorized, but if you don’t, you can ask yourself “what number times itself will give me ____?”. To calculate the square root of any other number, you can use the square root button on your calculator.

Most importantly, you should know that squaring and taking the square root of a number are opposite operations. That is, you can undo one of the operations by doing the other. This has applications in many contexts, including when we use the Pythagorean Theorem to solve for an unknown side length, c, which we will do in the Measurement module.