Arithmetic and Pre-Algebra Practice

Build confidence with the basic math skills needed before college algebra. This section reviews negative numbers, order of operations, variables, simple equations, fractions, decimals, and percentages.

Skill 1: Working with Negative Numbers

Negative numbers show values below zero or movement in the opposite direction. When adding a positive and a negative number, subtract the smaller absolute value from the larger absolute value. Then keep the sign of the number with the larger absolute value.

Worked Example

Problem: -8 + 3

Step 1: Compare the sizes of 8 and 3.

8 is larger.

Step 2: Subtract:

8 - 3 = 5

Step 3: Keep the sign of the larger number.

The larger number was -8, so the answer is negative.

Answer: -5

Try These

  1. -5 + 9
  2. 12 - 15
  3. -7 + 2
  4. -10 + 6
  5. 4 - 11

Answer Key

  1. 4
  2. -3
  3. -5
  4. -4
  5. -7

Mastery Check

You are ready to move on when you can explain why the answer keeps the sign of the number with the larger absolute value.

Skill 2: Order of Operations

Order of operations tells us which math steps to complete first. Without an order, the same problem could give different answers. Use PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.

Worked Example

Problem: 6 + 4 × 3

Step 1: Multiplication comes before addition.

4 × 3 = 12

Step 2: Now add.

6 + 12 = 18

Answer: 18

Try These

  1. 8 + 2 × 5
  2. 10 - 3 × 2
  3. 4 + 6 ÷ 2
  4. 3 × 5 + 7
  5. 20 - 12 ÷ 4

Answer Key

  1. 18
  2. 4
  3. 7
  4. 22
  5. 17

Mastery Check

You are ready to move on when you can explain why multiplication and division must be completed before addition and subtraction.

Skill 3: Understanding Variables

A variable is a letter that represents a number. In algebra, letters such as x, y, a, or b can stand for unknown values or changing values. To evaluate an expression, replace the variable with the given number and simplify.

Worked Example

Problem: If x = 7, evaluate 2x + 5.

Step 1: Replace x with 7.

2x + 5 becomes 2(7) + 5

Step 2: Multiply first.

2(7) = 14

Step 3: Add.

14 + 5 = 19

Answer: 19

Try These

  1. If x = 4, evaluate 3x - 1.
  2. If y = 6, evaluate 2y + 8.
  3. If a = 5, evaluate a + 12.
  4. If b = 3, evaluate 4b - 2.
  5. If n = 10, evaluate n ÷ 2 + 7.

Answer Key

  1. 11
  2. 20
  3. 17
  4. 10
  5. 12

Mastery Check

You are ready to move on when you can replace a variable with a number and simplify the expression using the correct order of operations.

Skill 4: Solving Simple Equations

An equation says that two expressions are equal. Solving an equation means finding the value of the variable that makes the equation true. To solve, use opposite operations to isolate the variable.

Worked Example

Problem: Solve for x: x - 9 = 4

Step 1: The variable x has 9 subtracted from it.

Step 2: Use the opposite operation. Add 9 to both sides.

x - 9 + 9 = 4 + 9

Step 3: Simplify.

x = 13

Answer: x = 13

Try These

  1. x + 5 = 12
  2. x - 7 = 3
  3. x + 9 = 15
  4. x - 4 = 10
  5. x + 2 = 18

Answer Key

  1. x = 7
  2. x = 10
  3. x = 6
  4. x = 14
  5. x = 16

Mastery Check

You are ready to move on when you can explain how opposite operations help isolate the variable.

Skill 5: Fractions to Decimals

A fraction can be written as a decimal by dividing the numerator by the denominator. The numerator is the top number. The denominator is the bottom number.

Worked Example

Problem: Convert 3/4 to a decimal.

Step 1: Divide the numerator by the denominator.

3 ÷ 4 = 0.75

Answer: 3/4 = 0.75

Try These

  1. Convert 1/5 to a decimal.
  2. Convert 1/2 to a decimal.
  3. Convert 3/10 to a decimal.
  4. Convert 2/5 to a decimal.
  5. Convert 1/4 to a decimal.

Answer Key

  1. 0.2
  2. 0.5
  3. 0.3
  4. 0.4
  5. 0.25

Mastery Check

You are ready to move on when you can explain that a fraction bar means division.

Back to Practice by Skill Next: Linear Equations