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Question

Difficulty: EasyOrder of Operations and Number Properties

What is the value of the expression 18−3×4∣−2∣+1\frac{18 - 3 \times 4}{|-2| + 1}?

Answer: 2

Answer

The value of the expression is 2.
To evaluate the expression, we simplify the numerator and denominator separately first. In the numerator, we perform the multiplication before the subtraction: 18−3×4=18−12=618 - 3 \times 4 = 18 - 12 = 6. In the denominator, we evaluate the absolute value and then add: ∣−2∣+1=2+1=3|-2| + 1 = 2 + 1 = 3. Finally, we divide the simplified numerator by the simplified denominator: 63=2\frac{6}{3} = 2.

Step-by-Step Solution

1
Evaluate the multiplication in the numerator.
3×4=123 \times 4 = 12, leaving the numerator as 18−1218 - 12.
According to the order of operations, multiplication must be performed before subtraction.
2
Subtract the values in the numerator.
18−12=618 - 12 = 6.
Simplify the numerator expression completely.
3
Evaluate the absolute value in the denominator.
∣−2∣=2|-2| = 2, leaving the denominator as 2+12 + 1.
Absolute value represents the non-negative distance from zero, so ∣−2∣=2|-2| = 2.
4
Add the values in the denominator.
2+1=32 + 1 = 3.
Simplify the denominator expression completely.
5
Divide the numerator by the denominator.
63=2\frac{6}{3} = 2.
Compute the final fraction value.

Key Concept

Evaluating expressions using the order of operations (PEMDAS) and absolute value properties.
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Topics

Order of Operations and Number Properties

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