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Question

Difficulty: MediumDecimal Operations

What is the exact value of the expression −4.2+3.6×(1.5−2.7)-4.2 + 3.6 \times (1.5 - 2.7)?

  1. −8.52-8.52Answer
  2. B
    0.720.72
  3. C
    0.120.12
  4. D
    −4.74-4.74

Answer

The correct value is −8.52-8.52.
The correct answer follows the standard order of operations and proper arithmetic rules for decimals and integers. First, the subtraction inside the parentheses is calculated as 1.5−2.7=−1.21.5 - 2.7 = -1.2. Next, the multiplication is performed before the addition: 3.6×(−1.2)=−4.323.6 \times (-1.2) = -4.32. Finally, −4.32-4.32 is added to −4.2-4.2, making sure to properly align the decimal points, which yields −8.52-8.52.

Step-by-Step Solution

1
Evaluate the expression inside the parentheses.
1.5−2.7=−1.21.5 - 2.7 = -1.2
According to the order of operations (PEMDAS), operations inside parentheses must be completed first.
2
Multiply the result from step 1 by 3.63.6.
3.6×(−1.2)=−4.323.6 \times (-1.2) = -4.32
Multiplication takes precedence over addition.
3
Add −4.2-4.2 to the product from step 2.
−4.2+(−4.32)=−8.52-4.2 + (-4.32) = -8.52
This is the final remaining operation. Decimal points must be aligned vertically (−4.20+(−4.32)-4.20 + (-4.32)) to ensure correct addition.

Key Concept

Decimal Operations with Order of Operations
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Topics

Decimal Operations

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