Math Problem Statement

Evaluate the expressions provided on the worksheet using the given values.

Solution

Here are the solutions for the problems on the worksheet:

Part 1: Evaluate Each Expression

  1. 4÷224 \div 2^2 22=4, so 4÷4=12^2 = 4,\ \text{so } 4 \div 4 = 1 Answer: 11

  2. 6×466 \times 4 - 6 6×4=24, and 246=186 \times 4 = 24,\ \text{and } 24 - 6 = 18 Answer: 1818


Part 2: Evaluate Each Using the Values Given

  1. jk4jk - 4, where j=2j = 2 and k=5k = 5 jk=2×5=10, and 104=6jk = 2 \times 5 = 10,\ \text{and } 10 - 4 = 6 Answer: 66

  2. x(zz)x - (z - z), where x=3x = 3 and z=1z = 1 zz=0, so x0=3z - z = 0,\ \text{so } x - 0 = 3 Answer: 33

  3. hkkhk - k, where h=5h = 5 and k=3k = 3 hk=5×3=15, and 153=12hk = 5 \times 3 = 15,\ \text{and } 15 - 3 = 12 Answer: 1212

  4. x(yx)x - (y - x), where x=4x = 4 and y=4y = 4 yx=44=0, so x0=4y - x = 4 - 4 = 0,\ \text{so } x - 0 = 4 Answer: 44

  5. z2(xx)z - 2(x - x), where x=1x = 1 and z=5z = 5 xx=0, so 2×0=0, and z0=5x - x = 0,\ \text{so } 2 \times 0 = 0,\ \text{and } z - 0 = 5 Answer: 55

  6. y+6x4y + \frac{6 - x}{4}, where x=2x = 2 and y=4y = 4 6x=62=4, 44=1, and y+1=4+1=56 - x = 6 - 2 = 4,\ \frac{4}{4} = 1,\ \text{and } y + 1 = 4 + 1 = 5 Answer: 55

  7. b+ab4b + \frac{ab}{4}, where a=3a = 3 and b=4b = 4 ab=3×4=12, 124=3, and b+3=4+3=7ab = 3 \times 4 = 12,\ \frac{12}{4} = 3,\ \text{and } b + 3 = 4 + 3 = 7 Answer: 77

  8. y+5(x+z)y + 5 - (x + z), where x=2x = 2, y=5y = 5, and z=2z = 2 x+z=2+2=4, so y+54=5+54=6x + z = 2 + 2 = 4,\ \text{so } y + 5 - 4 = 5 + 5 - 4 = 6 Answer: 66


Do you want detailed step-by-step explanations for any of the problems?

Here are 5 related questions:

  1. Can you simplify expressions involving parentheses and fractions in other examples?
  2. How would the answers change if the given values were different?
  3. How do you evaluate powers and divisions simultaneously in more complex problems?
  4. Can you explain how parentheses affect the evaluation order in expressions?
  5. What are the common mistakes to avoid when evaluating expressions like these?

Tip: Always follow the order of operations (PEMDAS) to evaluate expressions correctly!

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Math Problem Analysis

Mathematical Concepts

Order of Operations (PEMDAS)
Simplification of expressions
Substitution of variables
Basic arithmetic operations

Formulas

Powers (a^b)
Division (a / b)
Addition and subtraction
Multiplication

Theorems

Order of Operations
Properties of arithmetic

Suitable Grade Level

Grades 6-8