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Difficulty: MediumOrder of Operations and Number Properties

Four mathematical expressions are shown below:

* Expression 1: 4×(5−3)322−15÷3\frac{4 \times (5 - 3)^3}{2^2} - 15 \div 3
* Expression 2: ∣−8−2∣×(3−5)2÷8|-8 - 2| \times (3 - 5)^2 \div 8
* Expression 3: 24−4×3+23÷424 - 4 \times 3 + 2^3 \div 4
* Expression 4: 3×(4−7)2−∣−24+6∣3 \times (4 - 7)^2 - | -2^4 + 6 |

Arrange these expressions in order from least to greatest value.

  1. 1Expression 1
  2. 2Expression 2
  3. 3Expression 3
  4. 4Expression 4

Answer

Expression 1, Expression 2, Expression 3, Expression 4
Evaluating each expression using the correct order of operations yields the values 3, 5, 14, and 17, respectively. Ordering these values from least to greatest gives the sequence of Expression 1, Expression 2, Expression 3, and Expression 4.

Step-by-Step Solution

1
Evaluate Expression 1: 4×(5−3)322−15÷3\frac{4 \times (5 - 3)^3}{2^2} - 15 \div 3
33
First simplify the expression inside the parentheses: 5−3=25 - 3 = 2. Next, evaluate the exponents: 23=82^3 = 8 and 22=42^2 = 4. Then perform multiplication and division from left to right: 4×84=324=8\frac{4 \times 8}{4} = \frac{32}{4} = 8 and 15÷3=515 \div 3 = 5. Finally, perform subtraction: 8−5=38 - 5 = 3.
2
Evaluate Expression 2: ∣−8−2∣×(3−5)2÷8|-8 - 2| \times (3 - 5)^2 \div 8
55
Simplify inside the absolute value brackets and parentheses first: −8−2=−10-8 - 2 = -10, and its absolute value is ∣−10∣=10|-10| = 10. Also, 3−5=−23 - 5 = -2. Next, evaluate the exponent: (−2)2=4(-2)^2 = 4. Then perform multiplication and division from left to right: 10×4=4010 \times 4 = 40, and 40÷8=540 \div 8 = 5.
3
Evaluate Expression 3: 24−4×3+23÷424 - 4 \times 3 + 2^3 \div 4
1414
Evaluate the exponent first: 23=82^3 = 8. Next, perform multiplication and division from left to right: 4×3=124 \times 3 = 12 and 8÷4=28 \div 4 = 2. Finally, perform addition and subtraction from left to right: 24−12+2=12+2=1424 - 12 + 2 = 12 + 2 = 14.
4
Evaluate Expression 4: 3×(4−7)2−∣−24+6∣3 \times (4 - 7)^2 - | -2^4 + 6 |
1717
Simplify inside the parentheses: 4−7=−34 - 7 = -3, and evaluate its square: (−3)2=9(-3)^2 = 9. Then multiply: 3×9=273 \times 9 = 27. For the absolute value expression, evaluate the exponent first: −24=−(24)=−16-2^4 = -(2^4) = -16. Add: −16+6=−10-16 + 6 = -10, and take its absolute value: ∣−10∣=10|-10| = 10. Finally, perform subtraction: 27−10=1727 - 10 = 17.
5
Compare the evaluated values to order the expressions from least to greatest.
3<5<14<173 < 5 < 14 < 17
Comparing the values gives the sequence: Expression 1 (value of 3), Expression 2 (value of 5), Expression 3 (value of 14), and Expression 4 (value of 17).

Key Concept

Order of Operations (PEMDAS)
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Topics

Order of Operations and Number Properties

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