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Instructions

Solve the following problems, showing your work where necessary. Pay close attention to negative signs, decimal points, and common denominators. Simplify all fractions and algebraic expressions.


Part 1: Integer Operations

Calculate the value of each expression.

  1. (-34) + 19 = ?
  2. 21 - (-15) = ?
  3. (-8) - 22 = ?
  4. -16 + (-25) = ?
  5. 150 - 320 = ?

Part 2: Decimal Arithmetic

Calculate the value of each expression. Be careful to align the decimal points.

  1. 351.8 + 92.47 = ?
  2. 88.2 - 19.551 = ?
  3. A diver is at a depth of -45.6 meters. She ascends 18.8 meters. What is her new depth?
  4. Your lunch bill is $23.85. You pay with two $20 bills. How much change do you receive?

Part 3: Fraction Arithmetic

Calculate the value of each expression. Express your answers as simplified fractions or mixed numbers.

  1. 5/8 + 1/6 = ?
  2. 7/9 - 2/3 = ?
  3. 4 1/2 + 2 3/5 = ?
  4. 5 1/4 - 1 5/6 = ?

Part 4: Simplifying Algebraic Expressions

Combine like terms to simplify each expression.

  1. (8x - 5y) + (3x + 9y)
  2. (12a + 7b - 4) + (-5a - 10b + 2)
  3. (6m - 2n) - (9m + 4n)
  4. (3x² + 5x - 8) - (7x² - 2x - 11)

Part 5: Word Problems

Read each problem carefully and solve.

  1. The stock price of a company started the day at $56.75 per share. During the day, it dropped by $4.10, and then later rose by $2.55. What was the final stock price at the end of the day?
  2. You are baking a cake and need a total of 4 1/2 cups of flour. You have already added 2 1/3 cups. How much more flour do you need to add?



Answer Key

Part 1: Integer Operations

  1. -15
  2. 36
  3. -30
  4. -41
  5. -170

Part 2: Decimal Arithmetic

  1. 444.27
  2. 68.649
  3. -45.6 + 18.8 = -26.8 meters
  4. $40.00 - $23.85 = $16.15

Part 3: Fraction Arithmetic

  1. 15/24 + 4/24 = 19/24
  2. 7/9 - 6/9 = 1/9
  3. 9/2 + 13/5 = 45/10 + 26/10 = 71/10 or 7 1/10
  4. 21/4 - 11/6 = 63/12 - 22/12 = 41/12 or 3 5/12

Part 4: Simplifying Algebraic Expressions

  1. 11x + 4y
  2. 7a - 3b - 2
  3. 6m - 2n - 9m - 4n = -3m - 6n
  4. 3x² + 5x - 8 - 7x² + 2x + 11 = -4x² + 7x + 3

Part 5: Word Problems

  1. $56.75 - $4.10 + $2.55 = $52.65 + $2.55 = $55.20
  2. 4 1/2 - 2 1/3 = 9/2 - 7/3 = 27/6 - 14/6 = 13/6 or 2 1/6 cups
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