Math Problem Statement

Evaluate the expression 4·5·2 + (-1)·3·(-2) + 1·4·0 - (-2)·5·1 - 0·3·4 - 2·4·(-1).

Solution

The expression in the image is:

=452+(1)3(2)+140(2)5103424(1)= 4 \cdot 5 \cdot 2 + (-1) \cdot 3 \cdot (-2) + 1 \cdot 4 \cdot 0 - (-2) \cdot 5 \cdot 1 - 0 \cdot 3 \cdot 4 - 2 \cdot 4 \cdot (-1)

Let’s break it down and solve it step-by-step:

Step 1: Calculate each term

  • 452=404 \cdot 5 \cdot 2 = 40
  • (1)3(2)=6(-1) \cdot 3 \cdot (-2) = 6 (because multiplying two negative numbers gives a positive result)
  • 140=01 \cdot 4 \cdot 0 = 0
  • (2)51=10(-2) \cdot 5 \cdot 1 = -10
  • 034=00 \cdot 3 \cdot 4 = 0
  • 24(1)=82 \cdot 4 \cdot (-1) = -8

Step 2: Combine the results

40+6+0(10)0840 + 6 + 0 - (-10) - 0 - 8

Step 3: Simplify the expression

40+6+108=4840 + 6 + 10 - 8 = 48

Thus, the value of the expression is 48.

Would you like more details on the steps, or have any questions?

Here are 5 questions to expand your knowledge:

  1. What are the rules for multiplying negative and positive numbers?
  2. How does multiplying by zero affect an expression?
  3. What is the significance of parentheses in mathematical operations?
  4. How can you apply the distributive property in expressions like this?
  5. What are the common pitfalls when handling multiple signs in calculations?

Tip: Always evaluate multiplication and division before addition and subtraction when solving expressions!

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Math Problem Analysis

Mathematical Concepts

Multiplication
Negative Numbers
Order of Operations

Formulas

Multiplication of integers
Order of operations (PEMDAS)

Theorems

Multiplication of negative and positive numbers results in a sign change
Multiplying by zero results in zero

Suitable Grade Level

Grades 6-8