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Chapter 1: Problem 120

\(-6(-2)(-3)(-4)(5)\)

Short Answer

Expert verified
The product of \(-6(-2)(-3)(-4)(5)\) is 720.

Step by step solution

01

Identifying the negative and positive numbers

The numbers to be multiplied are -6, -2, -3, -4, and 5. Of these, four are negative and one is positive.
02

Multiplication

First, consider the four negative numbers. According to the rule of multiplication, the product of an even number of negative numbers is a positive number. So, multiplying -6, -2, -3 and -4 together gives \(6 \times 2 \times 3 \times 4 = 144\). Now, multiply the result by 5 (a positive number) which yields \(144 \times 5 = 720\).
03

Sign of the product

Since the multiplication involves an even number of negative numbers and a positive number, the total product will be positive. Therefore, the answer is 720.

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Key Concepts

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

Negative Numbers
When dealing with negative numbers, it's important to grasp what they represent. Negative numbers are those less than zero. They have a minus sign (鈭�) in front of them and are used to signify values like debts or losses. In the exercise, we see several negatives like
  • -6
  • -2
  • -3
  • -4
Negative numbers are vital in mathematics and arise in various contexts. When you're encountering them in problems, pay special attention to their signs. This brings us right into the heart of multiplication with negatives.
Multiplication Rules
Multiplication is repeated addition. Negative numbers introduce some extra rules when multiplying.
  • When multipling two numbers and they have the same signs (both positive or both negative), the result is positive.
  • With different signs (one positive and one negative), the result is negative.
The multiplication rules are why -2 multiplied by -3 equals 6 (positive) and -4 multiplied by 5 equals -20 (negative). Once you understand these rules, you'll be better equipped to handle complex sequences of multiplication in problems.
Sign of a Product
The sign of a product follows straightforward logic based on the numbers involved.
  • If you multiply an even number of negative numbers, the product is positive.
  • An odd number of negative numbers results in a negative product.
In the original exercise, we multiplied four negative numbers and one positive number. Because four, an even number of negatives, are present, the product turned positive.When multiplying o \(-6 \times -2 \times -3 \times -4 \times 5 \), we find the product to be 720, which is positive.This stems from the rule that even counts of negatives result in positive products.

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Most popular questions from this chapter

\((16-5) \div(3-5)\)

\(181-\left(13 \cdot 3^{2}\right)\)

\(-(-6)^{3}\)

\(\frac{3+[15 \div(-3)]}{16}\)

\(1 \cdot 4=4\)
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