Rational Numbers Test Answer Key with Scoring – Grade 7

Question 1 Fractions to Decimals (2 points)

1. 130 ÷ 16 = 8 r 2; 20 ÷ 16 = 1 r 4; 40 ÷ 16 = 2 r 8; 80 ÷ 16 = 5 r 0. So 1316 = 0.8125.
2. 80 ÷ 15 = 5 r 5; 50 ÷ 15 = 3 r 5, and remainder 5 repeats. So 815 = 0.53̅.

Scoring: 1 point per part; 1 point each for the correct division and result.

Question 2 Terminate or Repeat (2 points)

1. 2760 = 920, and 20 = 2 · 2 · 5, so it terminates (0.45).
2. 1118 is in lowest terms and 18 = 2 · 3 · 3 contains a 3, so it repeats.

Scoring: 1 point per part, for the right type with a valid reason.

Question 3 Mixed Forms Arithmetic (2 points)

1. −5.25 + 3.8 = −1.45.
2. −0.9 × (−0.8) = 0.72.

Scoring: 1 point per part.

Question 4 Order of Operations (2 points)

Divide first: −0.375 ÷ (−1.5) = 0.25. Then add: 2.25 + 0.25 = 2.5.

Scoring: 1 point for the quotient, 1 point for the final sum.

Question 5 Distance on the Number Line (3 points)

P = −2.25 and Q = 1.5.

1. Distance = 1.5 − (−2.25) = 3.75. 3.75 units.
2. Midpoint = (−2.25 + 1.5) ÷ 2 = −0.75 ÷ 2 = −0.375 = −38. Check: 3.75 ÷ 2 = 1.875 from each end.

Scoring: 1 point for part a; part b: 1 point for the sum, 1 point for halving and converting to a fraction.

Question 6 Freezer Power Outage (3 points)

1. −4.5 + 3 × 2.75 = −4.5 + 8.25 = 3.75°F.
2. Cooling: 2 × 1.25 = 2.5. Final: 3.75 − 2.5 = 1.25°F.
3. Net change: 8.25 − 2.5 = +5.75°F. Check: −4.5 + 5.75 = 1.25.

Scoring: 1 point per part.

Question 7 Eleven and a Repeating Pattern (3 points)

1. 50 ÷ 11 = 4 r 6; 60 ÷ 11 = 5 r 5; 50 ÷ 11 = 4 r 6 again. The remainders 5 and 6 cycle, so 5/11 = 0.4̅5̅.
2. Odd places hold 4 and even places hold 5. The 20th place is even, so the digit is 5.

Scoring: part a, 1 point for correct divisions and 1 point for noticing the repeat; part b, 1 point.

Question 8 Robotics Club Budget (3 points)

1. −18.40 + 75 = $56.60.
2. 4 × 9.35 = 37.40. Then 56.60 − 37.40 = $19.20.
3. Kit = 19.20 ÷ 4 = 4.80. Final: 19.20 − 4.80 = $14.40.

Scoring: 1 point per part.