Multiplying and Dividing Rational Numbers

After studying this lesson, you will be able to:

• Multiply and divide rational numbers

Multiplication and Division Rule (be sure to learn this rule)

If the two rational numbers have the same sign , their product or quotient will be positive .

If the two rational numbers have different signs , their product or quotient will be negative .

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For example:

Positive x Positive = Positive

Negative x Negative = Positive

Positive x Negative = Negative

Example 1

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Since we are multiplying a negative times a positive, the answer will be negative. Remember, you dont need a common denominator when multiplying fractions. Therefore, the answer will be which reduces to .

Example 2 ( -3 )(4) Were multiplying a negative times a positive, therefore the answer will be -12.

Example 3 (-3x) ( -4y) Were multiplying a negative times a negative, therefore the answer will be 12xy. (Remember, you dont have to have like terms to multiply.)

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Example 4

Just as with adding and subtracting, work with two numbers at a time.

Multiplying the first two fractions will give us .

Multiplying

Multiplying (the fives cancel and a positive times a positive gives us a positive )

Multiplying

Example 5 ÷ 36 (-4)

Since were dividing numbers with the same signs, the answer will be positive 9.

Example 6

Since were dividing numbers with different signs, the answer will be -12.

Example 7

Since were dividing numbers with different signs, the answer will be negative. We are dividing fractions, so we have to use the rule for dividing fractions. That rule is multiply by the reciprocal. First, we change the division sign to multiplication and we find the reciprocal of the second fraction. Now our problem looks like this: . Multiplying will give us . (note: it does not matter if the negative sign is in the numerator, the denominator, or is in front of the fraction.)