Question

Evaluate the expression.\(-3|-3|\)

Short answer

The result of the expression \(-3|-3|\) is -9.

Step-by-step solution

Evaluate the absolute value

First, evaluate the absolute value function, denoted by the vertical bars. The number within the bars is -3. The absolute value of a number is always non-negative, so the absolute value of -3 is 3.

Multiply by -3

Now, we can replace \(-3|-3|\) with \(-3 * 3\). Performing this multiplication yields a result of -9.

Key concepts

Evaluating Expressions

When evaluating expressions, it is essential to understand the order and structure of mathematical symbols and operations. Each expression needs to be carefully interpreted according to the mathematical rules governing it.

In the given exercise \(-3|-3|\), the first step is to tackle the absolute value part within the vertical bars. The absolute value of any number represents its distance from zero on the number line, ignoring the direction. This means that it is always a non-negative number. Hence, the absolute value of \(-3\) is \(3\).

After addressing the absolute value, you then include the remaining parts of the expression, which leads to the multiplication operation being the next focal point.

Negative Numbers

Negative numbers can sometimes seem tricky, but they are simply numbers less than zero, located to the left of zero on the number line. When dealing with absolute values, negative numbers are transformed into their positive counterparts. This is because the absolute value reflects the magnitude without regard to the sign.

For example, if you start with the negative number \(-3\), as in our exercise, its absolute value is \(3\). This transformation is what allows you to proceed with the rest of the expression evaluation.

Understanding how negative numbers behave in different operations, especially during absolute value operations, plays a crucial role in solving expressions accurately.

Multiplication in Algebra

Multiplication in algebra might involve dealing with numbers as well as variables. In this context, we focus on numerical multiplication, particularly involving negative numbers.

When multiplying numbers, the sign of the product depends on the signs of the numbers involved. If you multiply a positive and a negative number, the result is negative. If both numbers are positive or both are negative, the result is positive.

In our expression \(-3 * 3\), you're multiplying a negative number \(-3\) by a positive number \(3\). This means the product will be negative. Therefore, the result is \(-9\).

This concept of sign interaction in multiplication is essential to solving algebraic expressions correctly.