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Difficulty: EasyOrder of Operations and Number Properties

Evaluate the following three mathematical expressions using the standard order of operations, and arrange them in order from least to greatest value.

  1. 1The expression (12−4)÷2(12 - 4) \div 2
  2. 2The expression 12÷(4−2)12 \div (4 - 2)
  3. 3The expression 12−4÷212 - 4 \div 2

Answer

The correct order of the expressions from least to greatest value is (12−4)÷2(12 - 4) \div 2 (value of 44), followed by 12÷(4−2)12 \div (4 - 2) (value of 66), and finally 12−4÷212 - 4 \div 2 (value of 1010).
Evaluating the expressions according to the order of operations results in values of 1010, 44, and 66. Since 4<6<104 < 6 < 10, the correct order from least to greatest value is (12−4)÷2(12 - 4) \div 2, then 12÷(4−2)12 \div (4 - 2), and lastly 12−4÷212 - 4 \div 2.

Step-by-Step Solution

1
Evaluate 12−4÷212 - 4 \div 2.
The value is 1010.
Division has higher precedence than subtraction, so divide 44 by 22 first, then subtract from 1212.
2
Evaluate (12−4)÷2(12 - 4) \div 2.
The value is 44.
Parentheses have the highest precedence, so evaluate the subtraction inside first, then perform the division.
3
Evaluate 12÷(4−2)12 \div (4 - 2).
The value is 66.
Evaluate the subtraction inside the parentheses first, then divide 1212 by the result.
4
Compare the calculated values to order the expressions from least to greatest.
The order of values is 4<6<104 < 6 < 10.
Arranging the evaluated values in ascending order gives the correct sequence of the expressions.

Key Concept

The standard order of operations (PEMDAS) requires operations in parentheses to be performed first, followed by multiplication and division from left to right, and then addition and subtraction from left to right.
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Topics

Order of Operations and Number Properties

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