Pre-Algebra Unit 1: Whole Numbers and Integers — Free Review Games.
This unit covers integer operations, absolute value and order of operations — essential concepts for Pre-Algebra. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers integer operations, absolute value and order of operations — essential concepts for Pre-Algebra. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Integer Operations
Students must be able to add, subtract, multiply, and divide positive and negative integers accurately. Sign rules for multiplication and division are heavily tested: same signs produce a positive result, different signs produce a negative result. Subtraction of integers is rewritten as adding the opposite.
Key Points
- Adding two negatives always gives a negative: (-3) + (-5) = -8
- Subtracting a negative is the same as adding a positive: 7 - (-4) = 7 + 4 = 11
- Multiplying or dividing two numbers with the same sign gives a positive result
- Multiplying or dividing two numbers with different signs gives a negative result
Evaluate: (-6) × 3 ÷ (-2)
First, multiply (-6) × 3 = -18, because the signs are different (negative × positive = negative). Then divide -18 ÷ (-2) = 9, because the signs are the same (negative ÷ negative = positive). The final answer is 9.
2 Absolute Value
Absolute value represents the distance a number is from zero on the number line, so it is always non-negative. Students must evaluate absolute value expressions and solve simple absolute value equations. Watch out for negative signs placed outside the absolute value bars, which are applied after evaluating.
Key Points
- |a| is always ≥ 0 for any real number a
- |-7| = 7 and |7| = 7, because both are 7 units from zero
- A negative sign outside the bars negates the result: -|5| = -5
- To solve |x| = 4, set up two cases: x = 4 or x = -4
Evaluate: -|(-3) + (-5)|
First, compute the expression inside the bars: (-3) + (-5) = -8. Next, apply the absolute value: |-8| = 8. Finally, apply the negative sign outside: -8. The final answer is -8.
3 Order Of Operations
Students must apply the correct order of operations (PEMDAS) to simplify expressions involving multiple operations. Exponents are evaluated before multiplication and division, which are performed left to right before addition and subtraction. Expressions inside grouping symbols such as parentheses or brackets are always simplified first.
Key Points
- Order: Parentheses → Exponents → Multiplication/Division (left to right) → Addition/Subtraction (left to right)
- Multiplication and division have equal priority and are worked left to right, not multiplication before division
- Addition and subtraction have equal priority and are also worked left to right
- A fraction bar acts as a grouping symbol: simplify the numerator and denominator separately before dividing
Evaluate: 3 + 2² × (8 - 5) ÷ 6
Start with the parentheses: (8 - 5) = 3, giving 3 + 2² × 3 ÷ 6. Next, apply the exponent: 2² = 4, giving 3 + 4 × 3 ÷ 6. Then multiply and divide left to right: 4 × 3 = 12, then 12 ÷ 6 = 2, giving 3 + 2. Finally, add: 3 + 2 = 5.
Questions, answered.
What is Whole Numbers and Integers?
Whole Numbers and Integers is Unit 1 of Pre-Algebra, covering integer operations, absolute value and order of operations.
How to study for Pre-Algebra Unit 1?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 25+ review questions across 5 different game modes.