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Question

Difficulty: MediumDecimal Operations

A student is asked to simplify the expression below.

8.4−2.1×(−3.2)+1.58.4 - 2.1 \times (-3.2) + 1.5

What is the correct simplified value?

  1. A
    -18.66
  2. B
    3.18
  3. C
    7.71
  4. 16.62Answer

Answer

The correct simplified value is 16.62.
The exact evaluation requires multiplying 2.1 by -3.2 first to obtain -6.72. The expression then becomes an addition problem (8.4+6.72+1.58.4 + 6.72 + 1.5). Properly aligning the decimal points and summing these terms yields the true simplified value of 16.62.

Step-by-Step Solution

1
Identify and perform the multiplication operation first.
2.1×(−3.2)=−6.722.1 \times (-3.2) = -6.72
Following the order of operations (PEMDAS), multiplication takes precedence over addition and subtraction.
2
Substitute the product back into the expression and resolve the subtraction of a negative value.
8.4−(−6.72)+1.5=8.4+6.72+1.58.4 - (-6.72) + 1.5 = 8.4 + 6.72 + 1.5
Subtracting a negative number is mathematically identical to adding its positive counterpart.
3
Perform the addition operations from left to right, making sure to properly align the decimal points.
8.40+6.72+1.50=16.628.40 + 6.72 + 1.50 = 16.62
Addition operations are performed sequentially from left to right once all higher-priority operations are resolved, requiring proper place-value alignment.

Key Concept

Decimal Arithmetic and Order of Operations
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Topics

Decimal Operations

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