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Chapter 15: Problem 35

Simplify. $$ 3 \cdot(-2) \cdot(-1) \cdot(-1) $$

Short Answer

Expert verified
-6

Step by step solution

01

Multiply the first two numbers

Start by multiplying the first two numbers: \[ 3 \times (-2) = -6 \]
02

Multiply the result by the third number

Take the result from Step 1 and multiply it by the third number: \[ -6 \times (-1) = 6 \]
03

Multiply the result by the fourth number

Take the result from Step 2 and multiply it by the fourth number: \[ 6 \times (-1) = -6 \]

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Key Concepts

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

multiplication of integers
When working with multiplication, especially with integers, there are a few rules to keep in mind. Integers include all positive and negative whole numbers, along with zero. Multiplying two integers follows clear rules:
  • The product of two positive integers is positive: \( 3 \times 2 = 6 \)
  • The product of two negative integers is positive: \( -3 \times -2 = 6 \)
  • The product of a positive integer and a negative integer is negative: \( 3 \times -2 = -6 \)
So when simplifying expressions with multiplied integers, remember to apply these rules for each pair of integers you are multiplying. This basic concept will help you quickly determine the sign and value of products in your expressions.
negative numbers
Negative numbers can seem tricky, but understanding how they interact is essential for simplifying expressions. Whenever you multiply or divide negative numbers, the sign of the result depends on the signs of the numbers being used. Here are some key tips:
  • When you multiply two negative numbers, the product is positive. Think of multiplying -1 by -1: \((-1) \times (-1) = 1\), just like two negatives cancel out.
  • If a negative number is multiplied by a positive number, the result is negative: \((-3) \times 2 = -6\). The negative sign stays even after the multiplication.
  • Remember the rule: even number of negative numbers in multiplication gives a positive result, odd number gives a negative result.
This approach helps predict the signs without actually performing the entire calculation right away. It also helps in cross-checking if an answered sign makes sense.
step-by-step algebra
Step-by-step algebra is a powerful method to solve problems in a structured and clear manner. Tackling problems in small, manageable steps ensures accuracy and understanding. Let鈥檚 dissect our example: Simplify: \(3 \times (-2) \times (-1) \times (-1)\). Here's how to do it step by step:
  • Step 1: Multiply the first two numbers: \(3 \times -2 = -6\). First handle just these two numbers.
  • Step 2: Multiply the result by the third number: \(-6 \times -1 = 6\). Notice how multiplying these two negatives turns positive.
  • Step 3: Multiply the resulting positive by the last number: \(6 \times -1 = -6\). Final result remains true to our negative number rules.
Breaking each multiplication down ensures fewer mistakes and a deeper understanding. You can see exactly where negative numbers change the outcome and verify each step as you progress.

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