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Chapter 1: Problem 17

Evaluate each of the given expressions by performing the indicated operations. $$-2(4)(-5)$$

Short Answer

Expert verified
The expression evaluates to 40.

Step by step solution

01

Multiply the First Two Numbers

Start by multiplying the first two numbers in the expression: \(-2 \times 4 = -8\)
02

Multiply the Result with the Third Number

Take the result from Step 1 and multiply it by the third number: \(-8 \times (-5) = 40\). When multiplying two negative numbers, the result is positive.
03

Final Result

The final result is 40, so the value of the expression \(-2(4)(-5)\) is 40.

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Key Concepts

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

Multiplying Negative Numbers
When dealing with negative numbers, understanding how they interact during multiplication can be crucial. Negative numbers have a special property when multiplied:
  • If you multiply a negative number by a positive number, the result is always negative. For example, \(-2 \times 4 = -8\).
  • Conversely, when you multiply two negative numbers, the negatives "cancel out," resulting in a positive number. This happens because of the rule: \((-a) \times (-b) = ab\). For example, \(-8 \times (-5) = 40\).
Remember, negative times negative gives a positive. This property is essential for understanding and solving problems involving negative numbers.
Order of Operations
In math, expressions can become complicated quickly. To tackle them effectively, you need a clear process. This process is known as the order of operations, often remembered by the acronym PEMDAS:
  • P: Parentheses first
  • E: Exponents (powers and roots)
  • M and D: Multiplication and Division (left to right)
  • A and S: Addition and Subtraction (left to right)
In expressions like \(-2(4)(-5)\), you should proceed by tackling multiplication from left to right. Ensure you perform all operations inside parentheses first, but since there are no parentheses grouping our numbers here, move from left to right carefully with multiplication. Correct order of operations ensures you obtain the accurate result.
Integer Multiplication
Multiplying integers follows basic rules of arithmetic but keeping an eye out for the signs (positive or negative) makes it unique. Here鈥檚 a simple breakdown:
  • Multiplication is commutative, meaning that changing the order of the factors doesn鈥檛 change the product. For example, \(-2 \times 4\) is equivalent to \(4 \times -2\).
  • Be cautious of the signs. A mix of negative and positive integers results in a negative product.
  • When your multiplying consecutive negatives, such as in the last part from the solution\((-8)\times (-5)=40\), the negative signs cancel, giving a positive product.
Approaching integer multiplication with these in mind helps ensure accuracy in calculations and prevents mistakes, especially when dealing with complex expressions.

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