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Mathematical Reasoning Arithmetic and Number Sense Flashcards

6 cards from real GED practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 Mathematical Reasoning Arithmetic and Number Sense flashcards as text

  1. Evaluate: 3² − (12 ÷ 4 + 1)² × 2

    Answer: -23

    Following the strict order of operations (PEMDAS): first simplify inside the parentheses — 12 ÷ 4 = 3, then 3 + 1 = 4. Next, apply the exponents: 3² = 9 and 4² = 16. Then multiply: 16 × 2 = 32. Finally, subtract: 9 − 32 = −23. Common errors include forgetting to square the parenthetical result (giving 1) or omitting the final multiplication by 2 (giving −7).

  2. What is the result of (4.8 × 10⁵) ÷ (1.2 × 10⁻²), expressed in scientific notation?

    Answer: 4.0 × 10⁷

    Divide the coefficients: 4.8 ÷ 1.2 = 4.0. For the powers of 10, subtract the exponent in the denominator from the exponent in the numerator: 5 − (−2) = 5 + 2 = 7. The result is 4.0 × 10⁷. A frequent mistake is subtracting 5 − 2 = 3, giving the wrong answer of 10³.

  3. What is the sum of ALL integers that satisfy the inequality |2x − 3| ≤ 5?

    Answer: 9

    Split the absolute value inequality into a compound inequality: −5 ≤ 2x − 3 ≤ 5. Add 3 to all parts: −2 ≤ 2x ≤ 8. Divide by 2: −1 ≤ x ≤ 4. The integers in this range are −1, 0, 1, 2, 3, and 4. Their sum is −1 + 0 + 1 + 2 + 3 + 4 = 9.

  4. Which of the following numbers is rational?

    Answer: √(9/16)

    A rational number can be expressed as a ratio of two integers. √(9/16) = √9 ÷ √16 = 3 ÷ 4 = 3/4, which is a ratio of integers — so it is rational. √7 and √5 + √3 are irrational because 7 and 5 are not perfect squares. π is transcendental (irrational), so π ÷ 4 remains irrational.

  5. Simplify: (3/4 ÷ 5/8) − (1/3 × 9/4)

    Answer: 9/20

    First division: 3/4 ÷ 5/8 = 3/4 × 8/5 = 24/20 = 6/5. First multiplication: 1/3 × 9/4 = 9/12 = 3/4. Now subtract: 6/5 − 3/4. Find a common denominator of 20: 24/20 − 15/20 = 9/20.

  6. Three automated alarms at a facility sound every 8, 12, and 18 minutes, respectively. If all three sound together at 6:00 AM, at what time will they next all sound together?

    Answer: 7:12 AM

    Find the LCM of 8, 12, and 18. Prime factorizations: 8 = 2³, 12 = 2² × 3, 18 = 2 × 3². The LCM takes the highest power of each prime: 2³ × 3² = 8 × 9 = 72 minutes. Adding 72 minutes to 6:00 AM gives 7:12 AM. A common error is taking the GCF (2) or simply averaging the intervals.