Math Problem Statement

Negative numbers multiple-choice and short-answer questions from a math worksheet.

Solution

Let's go over the answers step by step for each question from the image you uploaded:

Multiple-choice questions:

  1. Which of the following statements is incorrect?

    • A: 2<4-2 < -4 is false (so it's incorrect).
    • Correct Answer: A.
  2. 12 + (-9) - (-3) is the same as:

    • This simplifies to 129+3=129+3=612 - 9 + 3 = 12 - 9 + 3 = 6.
    • Correct Answer: B is correct.
  3. If a=3a = -3, the value of 2a2-2a^2 is:

    • a2=(3)2=9a^2 = (-3)^2 = 9, so 2a2=2(9)=18-2a^2 = -2(9) = -18.
    • Correct Answer: D.
  4. The coordinates of the point that is 3 units below (3, 1):

    • Moving 3 units down means subtracting 3 from the y-coordinate: 13=21 - 3 = -2.
    • The new coordinates are (3, -2).
    • Correct Answer: E.
  5. 12 × (-4 + (-8) ÷ 2) equals:

    • Simplify the expression: 8÷2=4-8 ÷ 2 = -4, so 12×(4+(4))=12×(8)=9612 × (-4 + (-4)) = 12 × (-8) = -96.
    • Correct Answer: A.

Do you want further details on any of the solutions? Here are some related questions:

  1. Can you explain why 2<4-2 < -4 is false?
  2. What happens if you change the subtraction to addition in question 2?
  3. How do you determine the square of a negative number?
  4. How would the answer change in question 4 if we moved 3 units up instead of down?
  5. How does division affect the operation inside the parentheses in question 5?

Tip: Always simplify expressions inside parentheses first, especially when they involve division or multiplication, to avoid calculation errors.

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Math Problem Analysis

Mathematical Concepts

Inequalities
Integer Operations
Coordinate Geometry
Algebraic Expressions
Multiplication and Division of Integers

Formulas

Multiplication of negative numbers
Square of a number
Addition and subtraction of integers

Theorems

Order of operations (PEMDAS)

Suitable Grade Level

Grades 6-8