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BMST - Basic Math and Science Fractions, Decimals, and Number Operations Questions and Answers Flashcards

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  1. A chemist combines 3⅙ liters of compound A with 1½ liters of compound B, then discards ⅝ of the total mixture. How many liters remain?

    Answer: 1.75 liters

    Step 1 — find the total: 3⅙ + 1½ = 19/6 + 9/6 = 28/6 = 14/3 liters. Step 2 — discard ⅝, so ⅜ remains: ⅜ × 14/3 = 42/24 = 7/4 = 1.75 liters.

  2. A technician measures one wire at 0.00475 meters and a second wire at 3.8 × 10⁻³ meters. What is their combined length in scientific notation?

    Answer: 8.55 × 10⁻³ meters

    Convert 0.00475 to 4.75 × 10⁻³. Both values now share the exponent 10⁻³, so add the coefficients: 4.75 + 3.80 = 8.55. Combined length = 8.55 × 10⁻³ meters.

  3. Dividing 7/12 by 14/9 produces a result equivalent to which decimal?

    Answer: 0.375

    Dividing by a fraction means multiplying by its reciprocal: 7/12 ÷ 14/9 = 7/12 × 9/14 = (7 × 9)/(12 × 14) = 63/168. Divide numerator and denominator by 21: 3/8 = 0.375.

  4. A storage tank holds 4⅗ gallons. After three equal draws of 1⅓ gallons each, how much remains? Express as a simplified fraction.

    Answer: ⅗ gallon

    Total consumed = 3 × 1⅓ = 3 × 4/3 = 12/3 = 4 gallons exactly. Starting volume: 4⅗ = 23/5. Subtract 4 = 20/5: 23/5 − 20/5 = 3/5 = ⅗ gallon remains.

  5. A blueprint uses a scale where 0.625 inches represents 5 feet. A wall measures 11.25 inches on the blueprint. What is the actual wall length?

    Answer: 90 feet

    Find the unit rate: 5 ÷ 0.625 = 8 feet per blueprint inch. Multiply: 11.25 × 8 = 90 feet.

  6. What is the value of (⅔)² ÷ (4/9) + 1⅛?

    Answer: 2⅛

    Apply the exponent first: (⅔)² = 4/9. Divide: 4/9 ÷ 4/9 = 1. Add: 1 + 1⅛ = 2⅛. The key trap is performing addition before division, which violates order of operations.