Problem 24 - Elementary Algebra

Question

Find the value of each of the following expressions. $$ 5(-6) $$

Step-by-Step Solution

Answer

Answer: -30

Step 1: Write down the given expression

The given expression is: $$ 5(-6) $$

Step 2: Perform the multiplication

Now, perform the multiplication between the two numbers, 5 and -6: $$ 5 \times (-6) = -30 $$

Step 3: Write the final answer

The value of the expression 5(-6) is -30.

Key Concepts

Understanding Negative Numbers

Negative numbers are numbers less than zero. They often represent opposites such as debts, losses, or directions on a number line. If you think of a number line, zero is in the middle. Positive numbers are on the right and negative numbers are on the left. For example:

• -1 is one unit to the left of zero
• -6 is six units to the left of zero

Negative numbers have special properties when it comes to operations like addition, subtraction, and multiplication. When multiplying two numbers, if one of them is negative, the product will be negative. This is what happens in the given problem, where 5 is multiplied by -6, resulting in -30.

Basic Principles of Algebra

Algebra involves working with symbols and letters to represent numbers and expressions. It helps us solve problems more easily by understanding relationships between different values. In this exercise, we are using algebraic thinking to solve an expression that involves multiplying a positive number by a negative number.
Algebraic expressions can contain variables (such as x or y) and constants (such as 5 or -6). However, in this exercise, we're dealing with constants. Using algebraic rules, we can simplify expressions and find solutions. Multiplying two numbers within an expression is a fundamental algebraic operation, leading us to the product of 5(-6) as -30.

Improving Problem Solving Skills

Effective problem solving in math requires understanding the problem, planning a strategy, and following through with calculations. Here are some tips to tackle similar problems:

• Understand the Operation: Recognize whether you are dealing with addition, subtraction, multiplication, or division.
• Know the Rules: For multiplication, remember that multiplying a positive number by a negative number yields a negative result.
• Check Your Work: After solving, review each step for any errors.
• Practice: Regular practice with different numbers boosts confidence and accuracy.

By applying these strategies, you can enhance your ability to solve algebraic problems involving negative numbers, just like multiplying 5 by -6 to get -30.