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Chapter 3: Problem 443

In the following exercises, multiply. $$ -9 \cdot 4 $$

Short Answer

Expert verified
-36

Step by step solution

01

Identify the multiplication operation

The problem involves multiplying two numbers: -9 and 4.
02

Multiply the absolute values

Ignore the signs temporarily and multiply the absolute values of the two numbers. The absolute values of -9 and 4 are 9 and 4, respectively. Multiply these: \[ 9 \times 4 = 36 \]
03

Determine the sign of the product

Since we are multiplying a negative number (-9) by a positive number (4), the result will be negative. Thus, the product of -9 and 4 is -36.

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Key Concepts

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

Absolute Value
Absolute value refers to the distance a number is from zero on a number line, regardless of direction. It is always non-negative.
To find the absolute value of a number, simply ignore its sign.
For example:
* The absolute value of -9 is 9, represented as \(|-9| = 9\).
* The absolute value of 4 is 4, represented as \(|4| = 4\).
In multiplication problems, determining the absolute value first can simplify the operation, as seen when we multiplied \(9 \times 4 = 36\).
Negative Numbers
Negative numbers are numbers less than zero.
They are often represented with a minus sign (-) in front.
When you multiply a negative number by a positive number, the product always takes the sign of the negative number.
In the exercise, -9 is a negative number.
When multiplying -9 by 4, the negative sign affects the product: \( -9 \times 4 = -36 \).
Remember: Multiplying two negative numbers results in a positive number, while multiplying a negative by a positive results in a negative.
Positive Numbers
Positive numbers are numbers greater than zero.
They are represented without any sign, or with a plus sign (+).
In mathematical operations, positive numbers follow the standard arithmetic rules.
In the exercise, 4 is a positive number, and it remains positive during multiplication.
Key points:
* When multiplying two positive numbers, the answer is positive.
* When multiplying a positive number by a negative number, the answer takes the negative sign.
In our exercise: \(-9 \times 4 \) results in a product of \(-36 \).

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Most popular questions from this chapter

In the following exercises, evaluate. $$ 35-a \text { when } a=-4 $$

In the following exercises, determine whether each number is a solution of the given equation. $$ 5 x-10=-35 $$ $$ \begin{array}{l}{\text { (a) } x=-9} \\ {\text { (b) } x=-5 \quad \text { (c) } x=5}\end{array} $$

In the following exercises, simplify each expression. $$ 14+82 $$

In the following exercises, simplify each expression. $$ 42-4(6-9) $$

In the following exercises, divide. $$ -120 \div(-6) $$
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