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Chapter 2: Problem 33

Multiply. $$(-11)(-4)(-2)$$

Short Answer

Expert verified
-88

Step by step solution

01

Understand the Problem

You need to multiply three negative numbers: \(-11\), \(-4\), and \(-2\).
02

Multiply the First Two Numbers

First, multiply the first two numbers: \(-11\) and \(-4\). \(-11\) \times \(-4\) = 44, because the product of two negative numbers is positive.
03

Multiply the Result by the Third Number

Next, multiply the result from Step 2 by the third number: 44 \times \(-2\). Since the result of a positive number and a negative number is negative, 44 \times \(-2\) = -88.

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Key Concepts

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

product of negative numbers
When multiplying negative numbers, it's essential to understand a basic rule: the product of two negative numbers is always positive. This might seem counterintuitive at first, but think of it as reversing a double negative. For example,
- when you multiply \(-11\) and \(-4\), you get 44.
The idea behind this is that a negative times a negative cancels out the negatives, leaving a positive result.
To sum up, remember:
  • A negative times a negative equals a positive.
step-by-step multiplication
Breaking the multiplication process into steps makes it manageable and easier to follow. Let鈥檚 take a look at our example multiplying \(-11\), \(-4\), and \(-2\).
  • Step 1: Start by multiplying the first two numbers: \(-11\) \(\times\) \(-4\). As explained earlier, \(-11\) \(\times\) \(-4\) = 44.

  • Step 2: Now, take the result from Step 1, which is 44, and multiply it by the third number: 44 \(\times\) \(-2\).

  • Since a positive number times a negative number gives a negative result, 44 \(\times\) \(-2\) = -88.
Following these steps ensures you don鈥檛 get overwhelmed and mitigates errors.
negative and positive numbers
Multiplying negative and positive numbers follows specific rules. Let鈥檚 break it down:
  • Negative Times Positive: When you multiply a negative number and a positive number, the result is always negative. E.g., \(-3\) \(\times\) 5 = \(-15\).

  • Positive Times Negative: Similarly, when you multiply a positive number and a negative number, the outcome is still negative. E.g., 6 \(\times\) \(-2\) = \(-12\).

  • Negative Times Negative: As mentioned before, multiplying two negative numbers results in a positive product. E.g., \(-4\) \(\times\) \(-7\) = 28.
Understanding these rules will help you tackle a wide range of multiplication problems involving negative and positive numbers.

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Most popular questions from this chapter

One of the most famous blizzards in the United States was the blizzard of \(1888 .\) In one part of Nebraska, the temperature plunged from \(40^{\circ} \mathrm{F}\) to \(-25^{\circ} \mathrm{F}\) in \(5 \mathrm{hr}\). What was the average change in temperature during this time?

Assume \(a>0\) (this means that \(a\) is positive) and \(b<0\) (this means that \(b\) is negative). Find the sign of each expression. $$-(b)$$

Find the range. The range of a set of numbers is the difference between the highest value and the lowest value. That is, range = highest - lowest. Low temperatures for 1 week in Anchorage \(\left(^{\circ} \mathrm{C}\right):-4^{\circ},-8^{\circ}, 0^{\circ}, 3^{\circ},-8^{\circ},-1^{\circ}, 2^{\circ}\)

Assume \(a>0\) (this means that \(a\) is positive) and \(b<0\) (this means that \(b\) is negative). Find the sign of each expression. $$b-a$$

Perform the indicated operation. $$-36 \div(-12)$$
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