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Chapter 1: Problem 24

\(|8(-3)(5)|\)

Short Answer

Expert verified
-120

Step by step solution

01

Multiply the Numbers

First calculate the product of the numbers 8, -3, and 5. That is \(8 \times -3 \times 5\).
02

Find the Absolute Value

After getting the product, find its absolute value. The absolute value of a number is the non-negative value of the number. This means if the product is negative, take the positive value. If it is already positive, the value remains the same.

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Key Concepts

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

Multiplying Integers
When multiplying integers, the process is straightforward, but it's important to understand the rules concerning the signs.
  • When you multiply two positive integers, the result is positive.
  • Two negative integers multiplied together will result in a positive product.
  • If you multiply a positive integer by a negative integer, the result will be negative.
  • Similarly, multiplying a negative integer by a positive integer also gives a negative product.
Let's apply these rules to our original problem: First, multiply 8 by -3. Since 8 is positive and -3 is negative, the result is -24.
Now, multiply this result, -24, by 5. Again, the rule states that when a negative is multiplied by a positive, the result is negative, so we get -120.
Negative Numbers
Negative numbers are values that are less than zero. They are often represented with a minus sign (-) in front.
  • They have a lower value than any positive number or zero.
  • Negative numbers are used to represent values such as debt, temperature below zero, or loss.
  • They follow specific mathematical rules, especially when combined with positive numbers.
  • One key rule is that a negative number subtracted from another negative number gives a positive result.
In operations involving multiplication, two negatives change to a positive, but only when both numbers multiplied are negative. In our multiplication, when -3 is multiplied by 5, it remains negative because one of the values is positive.
Positive Numbers
Positive numbers are all numbers greater than zero. They don鈥檛 have a sign in front, but sometimes a plus sign (+) is used for clarity.
  • They are used to describe quantities, distances, and time durations.
  • All standard arithmetic rules for addition, multiplication, and other operations apply directly to positive numbers.
  • When multiple positive numbers are multiplied together, the result is always positive.
In our problem, we initially had positive numbers, 8 and 5, involved in the multiplication. Despite the negative number influencing the sign, these positive values retain their characteristics and size, impacting the magnitude of the final product.

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Most popular questions from this chapter

\(\frac{5+[(-12) \div 4]}{24}\)

\((14-17) \cdot(13-19)\)

\(\frac{1.32+4(3.68)}{1.5}\)

\([127-(13+4)] \div 10\)

\((-1.2)^{3}\)
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