Rational Numbers Worksheet Answer Key – Grade 7

Problem 1 Terminating Fraction by Long Division

Divide 7.000 by 8: 70 ÷ 8 = 8 remainder 6; 60 ÷ 8 = 7 remainder 4; 40 ÷ 8 = 5 remainder 0.

78 = 0.875

Problem 2 Convert a Fraction Over 25

11 ÷ 25: 110 ÷ 25 = 4 remainder 10; 100 ÷ 25 = 4 remainder 0. Check: 0.44 × 25 = 11.

1125 = 0.44

Problem 3 A Repeating Ninth

50 ÷ 9 = 5 remainder 5, and the remainder 5 returns at once, so the digit 5 repeats.

59 = 0.555… = 0.5̅

Problem 4 Twelfths as Decimals

70 ÷ 12 = 5 remainder 10; 100 ÷ 12 = 8 remainder 4; 40 ÷ 12 = 3 remainder 4. The remainder 4 repeats, so the digit 3 repeats from then on.

712 = 0.583̅

Problem 5 Predict the Decimal Type

1. 40 = 2 · 2 · 2 · 5, only 2s and 5s: terminates.
2. 18 = 2 · 3 · 3 includes a 3: repeats.
3. 1435 reduces to 25, and 5 is allowed: terminates.
4. 22 = 2 · 11 includes an 11: repeats.

Problem 6 Mixed Number to Decimal

30 ÷ 11 = 2 remainder 8; 80 ÷ 11 = 7 remainder 3; the remainder 3 returns, so the block is 27. Add the whole number 2.

2311 = 2.2̅7̅

Problem 7 Fraction Versus Decimal

50 ÷ 7 = 7 remainder 1; 10 ÷ 7 = 1 remainder 3; 30 ÷ 7 = 4 remainder 2, so 57 = 0.714… which is more than 0.700.

57 is greater than 0.7.

Problem 8 Mixed Signs, One Sum

Write 534 as 5.75. Different signs: 5.75 − 3.4 = 2.35, and the larger size is positive.

2.35

Problem 9 Product of Two Negatives

Same signs give a positive product. 2.5 × 1.6 = 4.00 (2.5 × 1 = 2.5 and 2.5 × 0.6 = 1.5).

4

Problem 10 Dividing by a Negative Fraction

−3/5 = −0.6. Same signs give a positive quotient. 7.2 ÷ 0.6 = 72 ÷ 6 = 12.

12

Problem 11 Subtracting a Negative

Subtracting −1.25 means adding 1.25: −0.75 + 1.25 = 0.5, a move of 1.25 units to the right.

0.5, which equals 12.

Problem 12 Three Terms with Mixed Forms

Write the mixed number as 2.25. Then −4.5 + 2.25 = −2.25, and −2.25 + 0.8 = −1.45.

−1.45

Problem 13 Length of the Repeating Block

Remainders: 10 ÷ 7 = 1 r 3; 30 ÷ 7 = 4 r 2; 20 ÷ 7 = 2 r 6; 60 ÷ 7 = 8 r 4; 40 ÷ 7 = 5 r 5; 50 ÷ 7 = 7 r 1. The remainder 1 returns, so 1/7 = 0.142857 142857… and the block 142857 has 6 digits.

20 = 3 × 6 + 2, so the 20th digit is the 2nd digit of the block: 4.

6 digits; the 20th digit is 4

Problem 14 Nested Operations

−2/3 + 1/2 = −4/6 + 3/6 = −1/6. Then −1/6 ÷ (−1/4) = 1/6 × 4 = 4/6.

23 = 0.6̅

Problem 15 Morning Temperature Swings

−8.5 + 17.75 = 9.25 at noon. Then 9.25 − 5.2 = 4.05.

4.05°F

Problem 16 Overdrawn Account

−23.40 + 60 = 36.60. Bills: 3 × 12.85 = 38.55. Then 36.60 − 38.55 = −1.95.

−$1.95 (the account is overdrawn by $1.95)

Problem 17 Rice for the Food Truck

1234 = 12.75. Divide: 12.75 ÷ 0.375 = 12,750 ÷ 375 = 34. Check: 34 × 0.375 = 12.75.

34 servings

Problem 18 Drone Flight Height

Descent: −2.75 × 8 = −22. Climb: 1.5 × 6 = 9. Height: 45 − 22 + 9 = 32.

32 feet

Problem 19 Net Yardage per Play

Net: −3.5 + 8.25 = 4.75; 4.75 − 2.75 = 2; 2 + 11 = 13; 13 − 0.5 = 12.5. Mean: 12.5 ÷ 5 = 2.5.

Net 12.5 yards; mean 2.5 yards per play

Problem 20 Splitting the Tab

86.50 ÷ 6: 6 × 14 = 84, remainder 2.5. Then 2.5 ÷ 6 = 0.41666…, so each share is 14.41666… = 14.416̅.

Rounded: $14.42. Total paid: 6 × 14.42 = 86.52, which is 86.52 − 86.50 = 0.02 too much.

Share = $14.416̅ ≈ $14.42; the group overpays by $0.02