Testinar Grade 7 math

Rational Number Operations in Extended Contexts

Students will build Grade 7 mastery of rational number operations in extended contexts using models, equations, and test-style reasoning.

CH03-10 The Number System
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. A scuba diver descends at a rate of \(-1.5\) meters per second. How long does it take to reach a depth of \(-18\) meters from the surface?

    1. \(9\) seconds
    2. \(12\) seconds
    3. \(16.5\) seconds
    4. \(27\) seconds

  2. An ocean temperature is changing at a rate of -0.3°C per hour. If the current temperature is 12°C, what will the temperature be after 5 hours?

    1. 10.5°C
    2. 13.5°C
    3. 11.5°C
    4. 12.3°C

  3. Maria's bank account has a balance of \($85.50\). She withdraws \($12.75\) twice in one week. What is her new balance?

    1. \($59.00\)
    2. \($72.75\)
    3. \($60.00\)
    4. \($97.00\)

  4. A football team gains 15 yards on first down, loses 4 yards on second down, then gains 8 yards on third down. What is the net yardage change for this series?

    1. \(19\) yards
    2. \(11\) yards
    3. \(27\) yards
    4. \(7\) yards

  5. A hiker is at an elevation of \(1,450\) feet. She climbs up \(325\) feet, then descends \(180\) feet. What is her final elevation?

    1. \(1,595\) feet
    2. \(1,270\) feet
    3. \(1,450\) feet
    4. \(1,955\) feet

  6. A swimmer completes laps in \(\frac{3}{4}\) minute during the first 9 minutes. Then her pace slows and she takes \(\frac{7}{8}\) minute per lap for the next 7 minutes. How many total laps does she complete?

    1. \(20\) laps
    2. \(20.5\) laps
    3. \(20.8\) laps
    4. \(19.5\) laps

  7. A recipe calls for \(\frac{2}{3}\) cup of sugar and \(\frac{3}{4}\) cup of flour. If you make 2 batches, then use \(\frac{1}{2}\) of that total sugar for a second dessert, how much sugar remains?

    1. \(\frac{2}{3}\) cups
    2. \(\frac{1}{3}\) cup
    3. \(1\) cup
    4. \(1\frac{1}{3}\) cups

  8. A temperature reading shows -5°F in the morning. By afternoon, the temperature increases by 18°F. What is the afternoon temperature?

    1. -23°F
    2. 13°F
    3. 23°F
    4. -13°F
Teacher and parent reference

Answer key and explanations

  1. B. \(12\) seconds

    Time \(=\) distance \(\div\) rate. The diver descends \(18\) meters at \(1.5\) m/s: \(18\div1.5=12\) seconds.

  2. A. 10.5°C

    Temperature change \(= -0.3 \times 5 = -1.5°\)C. New temperature \(= 12 + (-1.5) = 10.5°\)C.

  3. A. \($59.00\)

    Two withdrawals: \(-$12.75 - $12.75 = -$25.50\). New balance: \($85.50 - $25.50 = $59.00\).

  4. A. \(19\) yards

    Net change \(= 15 - 4 + 8 = 19\) yards.

  5. A. \(1,595\) feet

    Final elevation \(= 1,450 + 325 - 180 = 1,595\) feet.

  6. A. \(20\) laps

    First 9 minutes: \(9 \div \frac{3}{4} = 12\) laps. Next 7 minutes: \(7 \div \frac{7}{8} = 8\) laps. Total: \(12 + 8 = 20\) laps.

  7. A. \(\frac{2}{3}\) cups

    Total sugar for 2 batches \(= 2 \times \frac{2}{3} = \frac{4}{3}\) cups. Sugar used for second dessert \(= \frac{1}{2} \times \frac{4}{3} = \frac{2}{3}\) cups. Remaining \(= \frac{4}{3} - \frac{2}{3} = \frac{2}{3}\) cups.

  8. B. 13°F

    Afternoon temperature \(= -5 + 18 = 13°\)F.

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