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Question

Difficulty: EasyOrder of Operations

What is the exact value of the following mathematical expression?

10−(−2)3+42 \frac{10 - (-2)}{3} + 4^2

Answer: 20

Answer

The correct value is 20.
The expression is correctly evaluated by first simplifying the numerator grouping 10−(−2)10 - (-2) to get 1212, dividing by 33 to obtain 44, evaluating the exponent 424^2 to get 1616, and finally adding the results together to reach 2020.

Step-by-Step Solution

1
Simplify the grouping symbol formed by the numerator.
10−(−2)=1210 - (-2) = 12
The numerator of a fraction acts as a grouping symbol and must be evaluated first.
2
Divide the simplified numerator by the denominator.
123=4\frac{12}{3} = 4
The fraction bar represents division, which should be completed before addition.
3
Evaluate the exponent.
42=164^2 = 16
According to the order of operations, exponents must be evaluated before addition.
4
Add the remaining values.
4+16=204 + 16 = 20
Addition is the final operation left in the expression.

Key Concept

Order of Operations with fractions and signed numbers
Estimated Time:45s
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Topics

Order of Operations

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