Problem 265 Multiply. $$ -4 \cdot 8 $$... [FREE SOLUTION]

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Chapter 1: Problem 265

Multiply. $$ -4 \cdot 8 $$

Short Answer

Expert verified

The product is $-32$.

Step by step solution

Understand the Problem

The problem requires multiplying two numbers: $-4$ and $8$.

Identify the Signs

Notice that one number is negative ($-4$) and the other number is positive ($8$).

Multiply the Absolute Values

Ignore the signs for now and multiply the absolute values: $4 \times 8 = 32$.

Determine the Sign of the Product

Since one number is negative and the other is positive, the product will be negative. Therefore, the product is $-32$.

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Key Concepts

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

Negative Numbers

Negative numbers might seem tricky, but they follow simple rules. In mathematics, negative numbers are numbers less than zero. They are represented with a minus sign (-) in front of the number. For example, -4 means 4 units below zero.
Negative numbers are used to describe values like temperatures below freezing, losses in finances, or elevations below sea level. They also follow special rules when being added, subtracted, multiplied, or divided. Understanding how these rules work is crucial for solving problems involving negative numbers.

Absolute Values

The absolute value of a number is its distance from zero on the number line, regardless of direction. In other words, it is always a positive number or zero. For example, the absolute value of -4 is 4, and the absolute value of 8 is 8. This concept is useful when you need to focus on the size of a number without considering its sign.
To find the absolute value of a number, simply remove the negative sign if it exists. This basic concept is important when performing operations like multiplication, as it helps simplify the process by dealing only with positive numbers first.

Product Sign Rules

When multiplying integers, the sign of the product depends on the signs of the numbers being multiplied. The rules are straightforward:

If both numbers are positive, the product is positive.
If both numbers are negative, the product is positive.
If one number is positive and the other is negative, the product is negative.

In our example, -4 and 8, one number is negative and the other is positive. According to the product sign rules, the product of a positive number and a negative number is negative. Hence, the product of -4 and 8 is -32. Remembering these rules will help you quickly determine the sign of the product in multiplication problems involving integers.

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91影视

Multiply. $$ -4 \cdot 8 $$

Short Answer

Step by step solution

Understand the Problem

Identify the Signs

Multiply the Absolute Values

Determine the Sign of the Product

Key Concepts

Negative Numbers

Absolute Values

Product Sign Rules

One App. One Place for Learning.

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