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.
- (-34) + 19 = ?
- 21 - (-15) = ?
- (-8) - 22 = ?
- -16 + (-25) = ?
- 150 - 320 = ?
Part 2: Decimal Arithmetic
Calculate the value of each expression. Be careful to align the decimal points.
- 351.8 + 92.47 = ?
- 88.2 - 19.551 = ?
- A diver is at a depth of -45.6 meters. She ascends 18.8 meters. What is her new depth?
- 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.
- 5/8 + 1/6 = ?
- 7/9 - 2/3 = ?
- 4 1/2 + 2 3/5 = ?
- 5 1/4 - 1 5/6 = ?
Part 4: Simplifying Algebraic Expressions
Combine like terms to simplify each expression.
- (8x - 5y) + (3x + 9y)
- (12a + 7b - 4) + (-5a - 10b + 2)
- (6m - 2n) - (9m + 4n)
- (3x² + 5x - 8) - (7x² - 2x - 11)
Part 5: Word Problems
Read each problem carefully and solve.
- 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?
- 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
- -15
- 36
- -30
- -41
- -170
Part 2: Decimal Arithmetic
- 444.27
- 68.649
- -45.6 + 18.8 = -26.8 meters
- $40.00 - $23.85 = $16.15
Part 3: Fraction Arithmetic
- 15/24 + 4/24 = 19/24
- 7/9 - 6/9 = 1/9
- 9/2 + 13/5 = 45/10 + 26/10 = 71/10 or 7 1/10
- 21/4 - 11/6 = 63/12 - 22/12 = 41/12 or 3 5/12
Part 4: Simplifying Algebraic Expressions
- 11x + 4y
- 7a - 3b - 2
- 6m - 2n - 9m - 4n = -3m - 6n
- 3x² + 5x - 8 - 7x² + 2x + 11 = -4x² + 7x + 3
Part 5: Word Problems
- $56.75 - $4.10 + $2.55 = $52.65 + $2.55 = $55.20
- 4 1/2 - 2 1/3 = 9/2 - 7/3 = 27/6 - 14/6 = 13/6 or 2 1/6 cups