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Chapter 1: Problem 271

Multiply. $$ -1(-14) $$

Short Answer

Expert verified
The answer is 14.

Step by step solution

01

Understand the Problem

The given problem is \(-1(-14)\). We need to multiply \(-1\) by \(-14\).
02

Rules of Multiplication for Negative Numbers

Recall the rule when multiplying two negative numbers. The product of two negative numbers is always a positive number.
03

Perform the Multiplication

Multiply the absolute values:\[1 \times 14 = 14\]. Since both numbers were negative, the product will be positive.

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Key Concepts

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

Negative Number Multiplication
When talking about negative number multiplication, it's crucial to grasp the underlying concepts.
Negative numbers are numbers less than zero, often indicated with a minus sign (-). Multiplying negative numbers follows a specific pattern based on the sign and magnitude of the numbers involved.
Here's a quick refresher:
  • If both numbers are negative, their product is positive.
  • If one number is negative and the other is positive, the product is negative.
  • If both numbers are positive, the product remains positive.
This means that multiplying \(-1(-14)\) will result in a positive value because the two negative signs cancel each other out. More on why that works in the next section.
Rules of Multiplication
The key rules of multiplication form the backbone of understanding more complex calculations.
Here are the rules simplified for clarity:
  • Positive 脳 Positive = Positive
  • Negative 脳 Negative = Positive
  • Positive 脳 Negative = Negative
  • Negative 脳 Positive = Negative
So, when we multiply two negative numbers, like in our given exercise \(-1(-14)\), each negative sign negates the other. This means the negative signs cancel each other out, leading to a positive product. Understanding and remembering these rules can make solving such problems much easier!
Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction.
It always turns a negative number into a positive one. The absolute value of \(-1\) is \1\, and the absolute value of \(-14\) is \14\.
In our exercise, we first find the absolute values of the numbers involved:
\1 \times 14 = 14\. Then, we apply the multiplication rules explained earlier. Since \(-1(-14)\) involves two negative numbers, the result is positive. Therefore, multiplying these absolute values gives us the final answer: \14\.

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