Page 63 - ArithBook5thEd ~ BCC

When two signed numbers are multiplied

• if the numbers have the same sign, the product is positive.
• if the numbers have opposite signs, the product is negative.

In both cases, the absolute value of the product is the productof
the individual absolute values.

In the examples and exercises below, we freely use all three ways of symbolizing multiplication: ·,
×, and juxtaposition. It is easiest to determine the sign of the product first, and then compute with
the absolute values.

Example 60. Multiply (−16) × 5.

Solution. (−16) × 5= −80 (negative since the numbers have opposite signs).
Example 61. Find the product (−11) · (−12).

Solution. (−11) · (−12) = 132 (positive since the numbers have the same signs).

Example 62. Find the product (−630)(−205).

Solution. The product is positive since the numbers have the same sign. Multiplying the absolute values,
we obtain

63 0

× 20 5
31 50
1260
1291 50

Recall the zero property,which states that
0 · x =0 and x · 0= 0, for any number x.

This remains true for signed numbers.
Example 63. (−17) · 0= 0.
Also, 1 continues to be the multiplicative identity ,that is,

1 · x = x and x · 1= x, for any number x.

Example 64. (−55) · 1= −55.
Multiplication, like addition, continues to be associative when extended to signed numbers. Thus
we can multiply several signed numbers without worrying how we group them for multiplication. One
consequence is that the sign of a product of several signed numbers can be quickly determined in advance
by simply determining whether the number of negative factors is even or odd.

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