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Zorluk: Çok zorOrder of Operations and Number Properties

Let the values of three mathematical expressions be represented by AA, BB, and CC, where:

A=−32−(−2−4)2÷3×2A = -3^2 - ( -2 - 4 )^2 \div 3 \times 2
B=∣−5−(−3)∣−24÷(−2)3×(4−7)B = |-5 - (-3)| - 2^4 \div (-2)^3 \times (4 - 7)
C=4−3×222−(−1)5×3C = \frac{4 - 3 \times 2^2}{2} - ( -1 )^5 \times 3

Arrange the expressions AA, BB, and CC in order from least to greatest numerical value.

  1. 1Expression AA
  2. 2Expression BB
  3. 3Expression CC

Cevap

Expression A, Expression B, Expression C
Evaluating each expression using correct PEMDAS order of operations yields A=−33A = -33, B=−4B = -4, and C=−1C = -1. Comparing these values gives the order from least to greatest as Expression A, followed by Expression B, followed by Expression C.

Adım Adım Çözüm

1
Evaluate Expression A by applying order of operations.
A=−33A = -33
Simplify the grouping (−2−4)=−6(-2 - 4) = -6. Then apply exponents: −32=−9-3^2 = -9 and (−6)2=36(-6)^2 = 36. Perform division and multiplication from left to right: 36÷3×2=12×2=2436 \div 3 \times 2 = 12 \times 2 = 24. Subtract to find −9−24=−33-9 - 24 = -33.
2
Evaluate Expression B by applying order of operations.
B=−4B = -4
Simplify grouping terms: ∣−5−(−3)∣=2|-5 - (-3)| = 2 and (4−7)=−3(4 - 7) = -3. Evaluate exponents: 24=162^4 = 16 and (−2)3=−8(-2)^3 = -8. Perform division and multiplication from left to right: 16÷(−8)×(−3)=−2×(−3)=616 \div (-8) \times (-3) = -2 \times (-3) = 6. Subtract: 2−6=−42 - 6 = -4.
3
Evaluate Expression C by applying order of operations.
C=−1C = -1
Simplify the numerator: 4−3×22=4−12=−84 - 3 \times 2^2 = 4 - 12 = -8, so the fraction is −4-4. Evaluate the exponent: (−1)5=−1(-1)^5 = -1. Multiply: −1×3=−3-1 \times 3 = -3. Subtract: −4−(−3)=−1-4 - (-3) = -1.
4
Compare the resulting values to determine the correct order from least to greatest.
Expression A (−33-33) < Expression B (−4-4) < Expression C (−1-1)
Comparing negative integers, −33-33 is the smallest value and −1-1 is the largest value.

Anahtar Kavram

Order of Operations and Number Properties
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