Problem 20 - Fundamentals of Mathematics

Question

Find the value of each of the following. Use a calculator to check each result. $$ (4)(-18) $$

Step-by-Step Solution

Answer

The result is -72.

Step 1: Understanding the problem

We need to find the product of 4 and -18. This means multiplying these two numbers together.

Step 2: Set up the multiplication

Write down the multiplication problem: \( 4 \times (-18) \). This shows that 4 is multiplied by -18.

Step 3: Multiply the numbers

Perform the multiplication: \( 4 \times (-18) = -72 \). Since one of the numbers is negative, the result will be negative.

Step 4: Verify with a calculator

Use a calculator to multiply 4 and -18 to confirm the result. Enter 4, the multiplication sign, -18, and check that the result is indeed -72.

Key Concepts

Negative numbers

When dealing with negative numbers, it's important to understand how they behave in mathematical operations. Negative numbers are less than zero and are often used to represent losses, debts, or below-zero temperatures. In multiplication, the sign of the result depends on the signs of the numbers being multiplied.

• When you multiply two positive numbers, the result is positive.
• When you multiply a positive number by a negative number, the result is negative.
• If both numbers are negative, the result is positive since a negative times a negative equals a positive.

Understanding the concept of negative numbers can help solve multiplication problems like the one in this exercise, where you're asked to find the product of 4 and -18.

Calculator verification

Always double-check your multiplication results using a calculator, especially when working with negative numbers. A calculator is a handy tool that ensures your math work is correct.

Here’s how to verify a multiplication problem with a calculator:

• Enter the first number. On your calculator, type in 4.
• Press the multiplication button (×), then enter the second number, -18, by pressing the negative sign followed by 18.
• Press the equals button (=). The calculator should display -72, confirming your manual calculation.

Calculator verification helps catch mistakes and reinforces your understanding of how multiplication rules apply, especially with negatives.

Multiplying integers

Multiplying integers follows straightforward rules, but it becomes a bit more interesting when negative signs are involved. Integers include all whole numbers, both positive and negative, including zero.

Here are some key points when multiplying integers:

• Regardless of order, the product of an integer is the same: this is known as the commutative property. For example, 4 × -18 is the same as -18 × 4.
• Always keep track of signs: Positive × Positive = Positive, Positive × Negative = Negative, and Negative × Negative = Positive.
• Practice is essential: The more you practice multiplying integers, the more comfortable you will become with these rules.

Understanding these concepts ensures accurate results when performing calculations like 4 × -18, yielding -72.