Problem 32 - Elementary Algebra

Question

Find the value of each of the following expressions. $$ (-6)(4) $$

Step-by-Step Solution

Answer

Answer: -24

Step 1: Multiply the Numbers

To find the value of the expression, multiply the given numbers: $$ (-6)(4) $$

Step 2: Apply Rule for Multiplication of Positive/Negative Integers

The rule for multiplication of positive/negative integers states that if the signs of the numbers being multiplied are the same (both positive or both negative), the product will be positive. If the signs are different (one positive and one negative), the product will be negative. In our case, we have one negative number and one positive number, so the product will be negative: $$ (-6)(4) = -24 $$ The value of the given expression is -24.

Key Concepts

Negative Numbers

Negative numbers are numbers that are less than zero, and they are typically represented with a minus sign (-).
They appear to the left of zero on the number line.
Negative numbers are used in various situations such as temperature below zero, depths below sea level, and loss in financial situations.

• In calculations, adding a negative number is like subtracting its positive counterpart.
• For example, adding -3 is the same as subtracting 3.
• When multiplying or dividing, the rules depend on the combination of negative and positive numbers being used.

Understanding negative numbers helps us grasp more complex mathematical concepts, including the multiplication of integers.

Positive Numbers

Positive numbers are greater than zero and have no sign or a plus sign (+) preceding them.
They are found to the right of zero on the number line and represent values above zero.
Examples include whole numbers like 1, 2, 3, as well as fractions and decimals like 0.5 or 1.25.

• Positive numbers are used for representing quantities, distances, profits, and heights.
• In calculations, multiplying and dividing positive numbers result in positive outcomes.
• Adding positive numbers increases the total, much like earning or saving money.

Grasping the nature of positive numbers is essential for dealing with the operations involving both positive and negative numbers.

Multiplication Rules

Multiplication rules for integers help determine the sign and value of the product.
Here's a simple breakdown of these rules:

• When multiplying two positive numbers, the result is a positive number. For example, \( 3 \times 4 = 12 \).
• When multiplying two negative numbers, the result is a positive number. For example, \( (-3) \times (-4) = 12 \).
• When multiplying a positive number and a negative number, the result is a negative number. For example, \( (-3) \times 4 = -12 \).

The rules are consistent and can be used to solve multiplication problems easily.
For expressions involving different signs, remember that a negative and a positive yield a negative product, just like in our exercise where \( (-6) \times 4 = -24 \).