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Chapter 1: Problem 3

Multiply and divide. $$ 2(-4)(-9) $$

Short Answer

Expert verified
The result is 72.

Step by step solution

01

Identify the operation sequence

The expression given is \(2(-4)(-9)\). This means we need to perform multiplication operations sequentially from left to right.
02

Multiply the first two numbers

To start solving, multiply \(2\) by \(-4\). Multiplying these gives \(2 \times (-4) = -8\).
03

Multiply the result by the next number

Next, use the result from Step 2 and multiply it by \(-9\). This gives us \(-8 \times (-9) = 72\), because multiplying two negative numbers results in a positive number.

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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 the numbers less than zero. In algebra, they are typically represented with a minus sign (e.g., -4, -9). These numbers are on the opposite side of the number line from positive numbers.

Here鈥檚 something super important to remember about them:
  • Adding a negative number is the same as subtracting its positive counterpart. For example, adding -4 is the same as subtracting 4.
  • Subtracting a negative number is like adding the positive version of that number. So, subtracting -9 equals adding 9.
  • When we work with negative numbers, especially in multiplication or division, the signs of the numbers have a significant impact on the final result.

Knowing these basics will help you avoid mistakes when performing operations.
Order of Operations
In math, the order of operations is crucial to obtaining the correct result. Without it, calculations could go haywire! The rule we use is abbreviated as PEMDAS, which stands for:
  • P: Parentheses first
  • E: Exponents (i.e., powers and square roots, etc.)
  • M: Multiplication
  • D: Division (left to right)
  • A: Addition
  • S: Subtraction (left to right)

Our given problem, \(2(-4)(-9)\), involves only multiplication, so we follow the operations from left to right. This keeps everything simple and straightforward!

Always follow this order to ensure your solutions are accurate but remember that when multiplication and division are together, they are equally prioritized and occur from left to right.
Signs of Numbers in Multiplication
The signs of numbers in multiplication have specific rules that decide whether your result ends up positive or negative. Here鈥檚 a simple way to remember it:
  • If both numbers have the same sign, the result is positive. This is true for both positive times positive, as well as negative times negative.
  • If the numbers have different signs, the result is negative. This applies when you multiply a positive number by a negative number, or vice versa.

For example, in our exercise \(2 \times (-4)\), the result is -8 because the signs differ. Then, when multiplying \(-8\) by \(-9\), since both numbers are negative, the product is positive 72.

Understanding these sign rules helps prevent errors when dealing with any multiplication involving negative numbers.

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Most popular questions from this chapter

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Research and discuss the history of the number zero.

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