Problem 36 - Elementary Algebra

Question

Simplify. $$ (-1) 21 $$

Step-by-Step Solution

Answer

The simplified expression is -21.

Step 1: Understand the Problem

We need to simplify the expression \((-1) \times 21\). This involves multiplying the number 21 by -1.

Step 2: Apply the Rules of Multiplication

When multiplying by -1, the sign of the number changes. Thus, \((-1) \times 21 = -21\).

Step 3: Verify the Result

Check if the steps make sense: multiplying a positive number by -1 gives us the negative of that number, confirming that \(-21\) is correct.

Key Concepts

Understanding Negative Numbers

Negative numbers are numbers less than zero. On the number line, they are to the left of zero and are often used to represent things like debts or below-zero temperatures. A negative number is often indicated by a minus sign (-) before the number.
For example:

• -3 is three less than zero.
• -10 could represent a $10 debt.

When working with negative numbers, it's important to remember that they represent the opposite value of their positive counterparts. So, -5 means the opposite of 5.

Mastering Multiplication Rules

Multiplication rules help simplify arithmetic operations involving whole numbers. Multiplying negative numbers follows specific rules:

• A positive times a positive: The result is positive. For example, \(3 \times 4 = 12\).
• A negative times a positive: The result is negative. This is seen in the expression \((-1) \times 21 = -21\).
• A positive times a negative: Similar to the above, the result is also negative.
• A negative times a negative: The result turns positive because the two negatives cancel each other out, like \((-2) \times (-4) = 8\).

Remembering these rules is key to solving multiplication problems with negative numbers correctly.

The Art of Simplification

Simplification means making an expression easier to understand by reducing it to its simplest form. In mathematical problems, this often involves applying arithmetic rules particularly when dealing with multiplication or division.
When simplifying expressions involving multiplication with negative numbers:

• Identify and apply multiplication rules.
• Reduce the problem step-by-step.
• Always double-check your result to ensure accuracy.

Using these methods can help you quickly and efficiently arrive at the correct answer, just like simplifying \((-1) \times 21 \) to get \-21\.