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Lesson 3: Multiplying and Dividing Rational Numbers — Practice Questions

  1. 1. The division equation $(-42) \div 6 = -7$ demonstrates the inverse relationship between division and multiplication. Which multiplication equation correctly represents this same relationship?

    • A. $6 \times (-7) = -42$
    • B. $(-42) \times 6 = -7$
    • C. $7 \times 6 = 42$
    • D. $(-7) \times (-6) = 42$
  2. 2. Calculate the value of the expression $(-72) \div 9$. The answer is ___.

  3. 3. Find the quotient of the two integers: $(-54) \div (-6) = $ ___.

  4. 4. A submarine's depth changed by $-120$ meters in 6 minutes. What was the average change in depth per minute, assuming a constant rate?

    • A. $-20$ meters
    • B. $20$ meters
    • C. $-720$ meters
    • D. $-114$ meters
  5. 5. Which statement best explains why $(-35) \div (-7)$ results in a positive number?

    • A. Because a negative number divided by a negative number is positive.
    • B. Because 35 is a multiple of 7.
    • C. Because division always results in a smaller number.
    • D. Because the divisor is negative.
  6. 6. A scooter moves at a constant velocity of 8 meters per second. If it starts at position zero, what is its position after 4 seconds? The final position is ___ meters.

  7. 7. A submarine starts at the surface (position zero) and dives with a velocity of -10 feet per second. What is its position after 6 seconds? The final position is ___ feet.

  8. 8. An object moves with a negative velocity for a positive amount of time. What will the sign of its final position be, assuming it starts at zero?

    • A. Positive
    • B. Negative
    • C. Zero
    • D. It depends on the numbers
  9. 9. A car backs out of a driveway with a velocity of -3 meters per second. Starting from position zero, its position after 5 seconds is ___ meters.

  10. 10. A cyclist travels east at a velocity of 12 kilometers per hour for 2 hours. If east is the positive direction, what is her final position from her starting point?

    • A. 24 km
    • B. -24 km
    • C. 14 km
    • D. 10 km