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Chapter 1: Problem 2

Multiply. \(-8(5)\)

Short Answer

Expert verified
The product of -8 and 5 is -40.

Step by step solution

01

Identify the Numbers

Begin by identifying the numbers involved in the multiplication. In this exercise, we need to multiply -8 and 5.
02

Use the Rule of Signs

For multiplication involving negative numbers, remember that the product of one negative and one positive number is negative. Here, -8 is negative and 5 is positive, so the result will be negative.
03

Multiply the Absolute Values

Multiply the absolute values of the numbers. The absolute value of -8 is 8 and for 5 it is 5. Calculate 8 times 5, which equals 40.
04

Apply the Sign

Since step 2 determined the result is negative, apply a negative sign to the result from step 3. Thus, the final answer is -40.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Rule of Signs
When multiplying integers, understanding the rule of signs helps us quickly find the sign of the product. The rule is straightforward:
  • The product of two positive numbers is positive.
  • The product of two negative numbers is positive because a negative times a negative gives a positive.
  • The product of one positive and one negative number is negative.
To make it simple, if the signs are the same, the result is positive, and if the signs are different, the result is negative. In our example with -8 and 5, they have different signs, so the product is negative.
Absolute Value
Absolute value is a crucial concept when dealing with negative numbers. It removes any sign and simply measures distance from zero on a number line.
  • The absolute value of a positive number is the number itself.
  • For a negative number like -8, the absolute value is 8.
  • For zero, the absolute value is also 0, as it is neither positive nor negative.
To find the result of our multiplication, we multiplies the absolute values: 8 (from -8) and 5. This equals 40. Absolute values help us determine the magnitude or size of numbers without considering their signs initially.
Negative Numbers
Negative numbers can seem tricky at first, especially in multiplication. They represent values less than zero.
Negative numbers often arise in contexts like temperature, below sea level measurements, and financial debts. When multiplying, the presence of negative numbers affects the sign and not the size of the result.
  • Negative indicates magnitude in the opposite direction from positive.
  • Multiplying by a negative number "flips" the direction, affecting the sign.
In multiplication, zero and negative numbers have special interactions as well. For example, any number multiplied by zero is zero, regardless of a negative sign. In this exercise, since we have -8, a negative number, our product reflects that with a negative sign, ending as -40.

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