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Chapter 10: Problem 1

Multiply. \(-8 \cdot 2\)

Short Answer

Expert verified
-16

Step by step solution

01

- Identify the Numbers

The numbers to be multiplied are -8 and 2. Observe that -8 is a negative number while 2 is a positive number.
02

- Multiply the Absolute Values

First, multiply the absolute values of the numbers. The absolute value of -8 is 8, and the absolute value of 2 is 2. So, calculate: \( 8 \times 2 = 16 \)
03

- Determine the Sign of the Product

Since one of the numbers is negative and the other is positive, the product will be negative. Therefore, the product of -8 and 2 is: \( -16 \)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Absolute Values
Absolute values are very important in mathematics. They tell us how far a number is from zero on the number line. It doesn't matter if the number is positive or negative, we only care about its distance from zero.

For example, the absolute value of -8 is 8, because -8 is 8 units away from zero. Similarly, the absolute value of 2 is just 2, because it is 2 units away from zero.
Learning to calculate absolute values helps simplify other operations, like multiplication. When multiplying, we first find the absolute values, multiply them, and then decide the sign of the result.
Dealing with Negative Numbers
Negative numbers can be tricky, but understanding a few simple rules can make them easier to work with. A negative number is any number less than zero, represented by a minus sign in front of it.

When multiplying numbers, if one of the numbers is negative and the other is positive, the product will be negative. For example, in this exercise, we multiply -8 (negative) by 2 (positive). We first find the absolute values and multiply them, which gives us 16. Then, since one number is negative and the other is positive, we know the result must be negative: -16.

This rule is consistent and works every time, even with larger or smaller numbers.
Understanding Positive Numbers
Positive numbers are the numbers greater than zero. They are much simpler to work with compared to negative numbers.

When multiplying two positive numbers, the product is always positive. For example, 2 times 3 is 6, and 5 times 4 is 20.

However, the importance of positive numbers is highlighted when they interact with negative numbers. As seen before, if you multiply a positive number by a negative number, the result is negative. But if you multiply a positive number with another positive number, the result is always positive. Keeping these basic rules in mind will make solving similar math problems much easier.

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Most popular questions from this chapter

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