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Chapter 1: Problem 4

Calculate and express each result in its simplest form:\((-3) \times(-4)\)

Short Answer

Expert verified
The product of \((-3) \times (-4)\) is 12.

Step by step solution

01

Understand the Problem

We are given the mathematical expression \((-3) \times (-4)\). The task is to multiply these two numbers and express the result in its simplest form.
02

Recall Negative Multiplication Rule

When multiplying two negative numbers, the result is positive. This is an important rule to remember when solving the exercise.
03

Calculate the Product

Apply the multiplication rule: \((-3) \times (-4) = 12\). Since both numbers are negative, the result is positive.
04

Write Final Result

The result of \((-3) \times (-4)\) is a positive 12. Therefore, the simplest form of the product is 12.

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Key Concepts

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

Multiplication Rules
Multiplication rules are fundamental when dealing with numbers in mathematics. For any two numbers, whether they are positive or negative, the multiplication process follows clear patterns. Here are the key multiplication rules:
  • If you multiply two positive numbers, the product is positive. For example, 3 times 4 equals 12.
  • If you multiply two negative numbers, the product is also positive. This happens because a negative times a negative "cancels out" to become positive. For instance, \(-3 \ imes -4 = 12\).
  • If you multiply a positive number by a negative number, the product is negative. An example of this is 3 times -4, which equals -12.
Understanding these rules will greatly help in solving any multiplication problems involving negative numbers.
Negative Numbers
Negative numbers represent values less than zero. They are often used to depict debts, temperatures below freezing, or any value that is considered in deficit.
  • On a number line, negative numbers are to the left of zero.
  • The more negative a number is, the smaller its value. For instance, -5 is less than -3.
When dealing with negative numbers, it's important to keep track of the signs. Operations involving negative numbers can change the sign of the result, such as two negatives making a positive product.
Simplifying Expressions
Simplifying expressions is the process of bringing a mathematical expression to its most basic form. This often involves reducing fractions, combining like terms, or performing operations to produce a final result that is clearer and easier to understand.
  • Check for common factors in terms and cancel them out (for fractions).
  • Combine similar terms if possible, for instance, combining \(3x + 2x\) into \(5x\).
  • Perform all indicated operations to reach a final number, as in multiplying \(-3 \ imes -4 = 12\).
The goal of simplifying is to make the expression as straightforward as possible, ensuring the final answer is easy to interpret and understand.

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