Problem 27 - Prealgebra and Introductory Algebra

Question

Multiply. $$-5 \cdot(23)$$

Step-by-Step Solution

Answer

So, \(-5 * 23 = -115\).

Step 1: Multiplication

First, multiply the absolute values of the numbers without considering the sign. So, we have \(5 * 23 = 115\).

Step 2: Apply Sign Rule

Next, apply the rule that a negative number multiplied by a positive number yields a negative number. Hence, \(-5 * 23 = -115\).

Key Concepts

Understanding Multiplication

Multiplication is about adding a number to itself, a certain number of times. Think of it like repeated addition. When you multiply two numbers, you are essentially determining how many times one number is used as an addend. Consider the problem

• In the expression \(-5 \cdot 23\) , the multiplication part involves combining groups of \(5\) , \(23 times\) .
• Forget about the negative sign for just a bit; we're focusing on the magnitude, \(5\) and \(23\) .

We'll tackle the sign separately, but multiplication is about figuring out how many times a number can fit into another.
When we multiply two numbers, the result is the product. Regardless of what the numbers represent, the multiplication process remains consistent. You find the product by adding.
So, \(5 * 23\ = 115\) says you have \(5\) added \(23\) times. It’s as straightforward as that!

What is Absolute Value?

Absolute value is a measure of how far a number is from zero on a number line. It’s like ignoring the 'direction' and focusing on the 'distance'.

• Every number has an absolute value, which is always non-negative.
• For example, the absolute value of \(-5\) is \(5\) , and the absolute value of \(23\) is \(23\) .

In terms of multiplication: It enables us to simplify calculations by dealing only with magnitudes. When you multiply, just focus on these absolute values first, ignoring any negative or positive signs. Ultimately, these signs will be considered through other rules.
So, start with \(5\) and \(23\) , multiplying them to get \(115\) . Then, incorporate the sign rules to find the final answer.

Applying the Sign Rule in Multiplication

Sign rules in multiplication help determine whether your product is positive or negative:

• A negative number times a positive number yields a negative result.
• A positive times a negative also results in a negative.
• A negative multiplied by a negative results in a positive.
• And, as expected, a positive times a positive gives a positive.

In our exercise, we have \(-5\) multiplied by \(23\) . Remember: focus on the sign after obtaining the magnitude part of it.
Since the numbers have differing signs (one negative and one positive), the outcome will be negative. Knowing the rule is like having a trusty guide that clarifies whether your multiplication will result in a positive or negative product. Therefore, \(-5 \cdot 23 = -115\) , because the multiplication of negative and positive is negative.