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Chapter 2: Problem 27

Find each product. $$-5(-4)(6)$$

Short Answer

Expert verified
The product is 120.

Step by step solution

01

Identify the Numbers & Operations

We are given the expression \(-5(-4)(6)\). We need to find the product, which means multiplying these numbers together.
02

Multiply the First Two Numbers

First, multiply the two negative numbers together. Calculating \(-5 \times -4 = 20\) because a negative times a negative is a positive.
03

Multiply by the Third Number

Next, take the result from Step 2 and multiply it by the third number: \(20 \times 6 = 120\).

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Key Concepts

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

Negative Numbers
Negative numbers are numbers less than zero, often marked on the number line to the left of zero. They are used in various mathematical operations, including integer multiplication. One important rule in math is that when you multiply two negative numbers, the product is positive. For example,
  • Multiplying \(-3\) and \(-2\) results in \(6\).
This occurs because multiplying with a negative number can be thought of as reversing the direction on the number line, and two reversals bring you back to a forward direction. So, in our example, multiplying \(-5\) and \(-4\) gives us a positive \(20\). On the other hand, multiplying a negative and a positive number results in a negative product, as only one reversal occurs.
Order of Operations
The order of operations is a critical concept in mathematics. It dictates the sequence in which you solve different parts of a mathematical expression. Typically, the order can be remembered by the acronym PEMDAS:
  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)
In our example, we have the expression \(-5(-4)(6)\). There are no parentheses that alter the basic operations order, and there are neither exponents nor addition or subtraction to consider. Therefore, multiplication, in this case, must be performed left to right.
  • First you multiply \(-5\) and \(-4\) to get \(20\),
  • then multiply the result by \(6\) resulting in \(120\).
Following these rules ensures accuracy in solving any mathematical expression.
Product of Numbers
The product of numbers refers to the result of multiplying two or more numbers. This operation is one of the four basic arithmetic operations and is symbolized often by \(\times\) or simply by juxtaposition. When you're given an expression like \(-5(-4)(6)\), you are being asked to find the product, that is, multiply all designated numbers. For instance,
  • The calculation begins by multiplying the first two numbers, \(-5\) and \(-4\), to obtain \(20\). As we've discussed, it's positive because two negative numbers are involved.
  • Next, this product, \(20\), is multiplied by \(6\) to arrive at the final product, which is \(120\).
Recognizing what the product is and how to methodologically find it is vital for solving mathematical problems, ensuring that each step follows the correct sequence as per the order of operations.

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