Problem 11 Multiply. $$ -3 \cdot 8 $$... [FREE SOLUTION]

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Chapter 1: Problem 11

Multiply. $$ -3 \cdot 8 $$

Short Answer

Expert verified

$ -24 $

Step by step solution

- Understand the Problem

The exercise requires multiplying two numbers: $-3$ and $8$.

- Identify the Signs

We need to determine the sign of the product. The multiplication of a negative number ($-3$) and a positive number ($8$) results in a negative product.

- Multiply the Absolute Values

Multiply the absolute values of the two numbers: $3$ and $8$. \[ 3 \times 8 = 24 \]

- Apply the Sign to the Product

Since the product of the multiplication involves a negative number and a positive number, the result is negative. So, $-3 \times 8 = -24 $.

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Key Concepts

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

negative numbers

Negative numbers are numbers less than zero. They are represented with a minus sign (-) preceding the number. When working with negative numbers, it helps to visualize them on a number line. For example, -3 is three units left from zero. Negative numbers are essential in various math problems and real-life situations like temperatures below freezing or financial debts. When you multiply or add negative numbers, there's a set of rules to follow. Understanding these rules is crucial to solving math problems accurately.

absolute value

The absolute value of a number is its distance from zero on the number line, regardless of its direction. For example, the absolute value of both -3 and 3 is 3, denoted as $|-3| = 3$. Absolute values are always non-negative. They essentially strip away the sign of the number. This property is helpful when multiplying or dividing negative numbers because it allows you to handle the magnitude without worrying about the sign until the end. In our example, simplifying \-3 \times 8\ involves finding \-3\'s absolute value first, which is 3.

multiplying integers

Multiplying integers involves a few straightforward steps. First, ignore the signs and multiply the absolute values of the numbers. In our example, multiplying $-3 \times 8 $, we first find \ 3 \times 8 = 24\. Next, determine the sign of the product. The rule is simple:

If you multiply two positive numbers, the result is positive.
If you multiply two negative numbers, the result is positive because two negatives cancel each other out.
If you multiply a negative number by a positive number, the result is negative.

Since \-3\ is negative and \8\ is positive, the result of their multiplication \-3 \times 8 \ is \-24\.

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91影视

Multiply. $$ -3 \cdot 8 $$

Short Answer

Step by step solution

- Understand the Problem

- Identify the Signs

- Multiply the Absolute Values

- Apply the Sign to the Product

Key Concepts

negative numbers

absolute value

multiplying integers

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