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Question

Difficulty: EasyOrder of Operations

Simplify the given mathematical expression. Which of the following represents its final value?

−5−3×(−2)+4 -5 - 3 \times (-2) + 4
  1. A
    -11
  2. B
    -7
  3. 5Answer
  4. D
    20

Answer

5
According to the order of operations, multiplication must be evaluated before addition and subtraction. First, multiply 3 by -2 to get -6. Subtracting this negative product from -5 gives -5 - (-6), which correctly simplifies to -5 + 6 = 1. Finally, add 4 to reach the correct final answer of 5.

Step-by-Step Solution

1
Identify the operations in the expression and determine their correct order of execution.
The expression contains subtraction, multiplication, and addition. Multiplication must be performed first.
According to the standard order of operations (PEMDAS), multiplication has a higher priority than addition and subtraction.
2
Perform the multiplication step.
3×(−2)=−63 \times (-2) = -6. The expression becomes −5−(−6)+4-5 - (-6) + 4.
Calculate the product before processing the outer subtraction.
3
Simplify the subtraction of a negative number.
−5−(−6)+4-5 - (-6) + 4 becomes −5+6+4-5 + 6 + 4.
Subtracting a negative integer is mathematically equivalent to adding its positive counterpart.
4
Evaluate the remaining addition and subtraction from left to right.
−5+6=1-5 + 6 = 1, and 1+4=51 + 4 = 5.
Addition and subtraction hold the same operational priority and are resolved sequentially from left to right.

Key Concept

Order of Operations with Signed Integers

Alternative Method

Instead of subtracting the product of 3 and -2, you can treat the subtraction symbol as a negative sign attached to the 3. This changes the multiplication step to (-3) * (-2) = 6. The entire expression then immediately becomes -5 + 6 + 4, which easily sums to 5.
Estimated Time:45s
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Topics

Order of Operations

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