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Chapter 1: Problem 25

perform the indicated multiplication. $$(-4)(-3)(-1)(6)$$

Short Answer

Expert verified
The result of (-4)(-3)(-1)(6) is -72.

Step by step solution

01

Multiplication Step 1

Begin by multiplying the first two numbers. Multiply -4 and -3. The multiplication of two negative numbers results in a positive number. Therefore, -4 multiplied by -3 equals to 12.
02

Multiplication Step 2

Next, multiply the result from step 1 with the next number. Multiply 12 with -1. The multiplication of a negative number and positive number results in a negative number. Therefore, 12 multiplied by -1 equals to -12.
03

Multiplication Step 3

Finally, multiply the result from step 2 with the final number. Multiply -12 with 6. Again, the multiplication of a positive number and a negative number results in a negative number. Therefore, -12 multiplied by 6 equals to -72.

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Key Concepts

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

Understanding Negative Numbers
Negative numbers are numbers with a value less than zero. The concept may seem tricky at first, but it's easier once you understand the rules that guide their operations.

When multiplying two numbers, the sign of the result depends on the signs of the numbers being multiplied.
  • If both numbers are negative, the product is positive. For example, multiplying \(-4 \times -3\) results in 12.
  • If one number is negative and the other is positive, the product is negative. For instance, multiplying \(12 \times -1\) results in -12.

Understanding these rules helps prevent mistakes when doing math involving negative numbers.
Positive Numbers in Multiplication
Positive numbers are numbers greater than zero. They are straightforward to work with as they follow predictable multiplication rules.

Here鈥檚 how multiplication works with positive numbers:
  • Multiplying a positive number with another positive number results in a positive number, such as \(6 \times 2 = 12\).
  • If multiplying a positive number with a negative number, the result will be negative, like \(6 \times -2 = -12\).

By understanding these basic rules, you can tackle more complex math problems with confidence.
Order of Operations in Math
The order of operations is crucial in ensuring that math problems are solved correctly. Following the wrong order can lead to incorrect results.

Here鈥檚 a quick rundown of the order of operations:
  • Perform calculations inside parentheses first. They take the highest priority.
  • Next, handle exponents (powers and roots).
  • Proceed with multiplication and division from left to right.
  • The final step is adding and subtracting from left to right.

In the given multiplication problem \((-4)(-3)(-1)(6)\), we perform multiplication from left to right after dealing with any parentheses, though none are included here. This approach ensures the computation is accurate and consistent every time.

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Most popular questions from this chapter

Write each English phrase as an algebraic expression. Let the variable \(x\) represent the number. nine subtracted from a number

Write a positive or negative integer that describes each situation. Banking: A withdrawal of \(\$ 3000.00\)

Express each rational number as a decimal. $$\frac{5}{16}$$

Perform the indicated division or state that the expression is undefined. $$-15 \div 3$$

In Exercises \(29-72,\) use the order of operations to simplify each expression. $$8^{2}-16 \div 2^{2} \cdot 4-3$$
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