Multiplication/Division

In a multiplication problem, those numbers (or later, variables) that are being multiplied are called factors; the result of a multiplication problem is called a product.

In algebra, multiplication is not indicated using the × sign (since × is often the variable of choice!). Instead, multiplication can be expressed using a dot, as in 2·3 = 6 (here, 2 and 3 are the factors and 6 is the product), or by using parentheses as in

(−7)(3) = −21.

In arithmetic, division is usually written as either 36 ÷ 4 = 9, or 

$4\begin{array}{c}\hfill 9\\ \hfill \overline{)36}\end{array}$

Using this example, 36 is known as the dividend, 4 is the divisor, and the result 9 is called the quotient.

In algebra, however, division is typically expressed in a fractional form.

The rules for multiplying and dividing signed numbers involve counting the number of negative signs in the problem. These rules apply to problems involving multiplication only, division only, or multiplication and division combined.

Use these rules to determine the sign of a product or quotient:  $\frac{36}{4}=9$ or $36/4=9$ .

— If there are an even number of negative signs, the product/quotient is positive.

— If there are an odd number of negative signs, the product/quotient is negative.

PLEASE NOTE:

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Example 1_7

$\left(-5\right)\left(-6\right)\left(-2\right)$

Example 1_7_2

$\frac{\left(-3\right)\left(-2\right)\left(4\right)}{\left(-2\right)\left(-2\right)}$

 

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