Problem 32 Multiply. See Example 2. $$ ... [FREE SOLUTION]

Chapter 1: Problem 32

Multiply. See Example 2. $$ (-2)(-5) $$

Short Answer

Expert verified

The product of $-2$ and $-5$ is 10.

Step by step solution

Understanding the Problem

The problem requires us to multiply two negative numbers: $-2$ and $-5$. In mathematics, the product of two numbers with the same sign is positive. Let's proceed with the calculation.

Multiplying the Absolute Values

First, we multiply the absolute values of the numbers. The absolute value of $-2$ is $2$, and the absolute value of $-5$ is $5$. So, we calculate $2 \times 5 = 10$.

Applying the Sign Rule

Since both numbers are negative, their product will be positive. Thus, the result of the multiplication $(-2) \times (-5) $ is positive 10.

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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 those with a "-" sign in front and are less than zero. They represent values on the left side of the zero on the number line.
For instance:

-1, -3.5, -7

Understanding negative numbers is crucial when performing mathematical operations such as addition, subtraction, and multiplication. They often describe situations where we have less of something, like owing money or being below a reference point such as sea level.

Absolute Value

The absolute value of a number is its distance from zero on the number line, without considering its sign. It's always a non-negative number.
To find the absolute value, you simply remove any negative sign:

The absolute value of $-4$ is $4$.
The absolute value of $3$ is $3$.

When multiplying integers, using absolute values allows us to ignore signs initially and focus on calculating the numerical product. After finding the product of the absolute values, we then reinstate the appropriate sign in the final answer.

Sign Rule in Multiplication

The sign rule in multiplication determines the sign of the product based on the signs of the numbers being multiplied. Here are the essential rules:

If both numbers have the same sign (either both positive or both negative), their product is positive. For example, $(-2) \times (-5)$ will yield a positive result.
If the numbers have different signs (one positive and one negative), their product is negative. For example, $3 \times (-4) = -12$.

Being familiar with these rules helps avoid mistakes when calculating products, especially in problems involving both positive and negative integers.

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91影视

Multiply. See Example 2. $$ (-2)(-5) $$

Short Answer

Step by step solution

Understanding the Problem

Multiplying the Absolute Values

Applying the Sign Rule

Key Concepts

Negative Numbers

Absolute Value

Sign Rule in Multiplication

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