ReasoningAges 16-18

Modular arithmetic & remainder cycles

Use division remainders (modulo arithmetic) to predict where a repeating cycle lands. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

1. Find the remainder when 82 is divided by 7.
82 · 7 · Modular arithmetic & remai…
2. Find the remainder when 143 is divided by 8.
143 · 8 · Modular arithmetic & remai…
3. Find the remainder when 44 is divided by 7.
44 · 7 · Modular arithmetic & remai…
4. Find the remainder when 94 is divided by 5.
94 · 5 · Modular arithmetic & remai…
5. Find the remainder when 76 is divided by 8.
76 · 8 · Modular arithmetic & remai…
6. Find the remainder when 68 is divided by 9.
68 · 9 · Modular arithmetic & remai…
7. Find the remainder when 121 is divided by 7.
121 · 7 · Modular arithmetic & remai…
8. Find the remainder when 123 is divided by 8.
123 · 8 · Modular arithmetic & remai…
9. Find the remainder when 113 is divided by 7.
113 · 7 · Modular arithmetic & remai…
10. Find the remainder when 59 is divided by 7.
59 · 7 · Modular arithmetic & remai…
11. Find the remainder when 188 is divided by 11.
188 · 11 · Modular arithmetic & remai…
12. Find the remainder when 79 is divided by 8.
79 · 8 · Modular arithmetic & remai…

12 questions · Seed 104731 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. Find the remainder when 82 is divided by 7.
5
82 = 7 × 11 + 5, so the remainder is 5.
2. Find the remainder when 143 is divided by 8.
7
143 = 8 × 17 + 7, so the remainder is 7.
3. Find the remainder when 44 is divided by 7.
2
44 = 7 × 6 + 2, so the remainder is 2.
4. Find the remainder when 94 is divided by 5.
4
94 = 5 × 18 + 4, so the remainder is 4.
5. Find the remainder when 76 is divided by 8.
4
76 = 8 × 9 + 4, so the remainder is 4.
6. Find the remainder when 68 is divided by 9.
5
68 = 9 × 7 + 5, so the remainder is 5.
7. Find the remainder when 121 is divided by 7.
2
121 = 7 × 17 + 2, so the remainder is 2.
8. Find the remainder when 123 is divided by 8.
3
123 = 8 × 15 + 3, so the remainder is 3.
9. Find the remainder when 113 is divided by 7.
1
113 = 7 × 16 + 1, so the remainder is 1.
10. Find the remainder when 59 is divided by 7.
3
59 = 7 × 8 + 3, so the remainder is 3.
11. Find the remainder when 188 is divided by 11.
1
188 = 11 × 17 + 1, so the remainder is 1.
12. Find the remainder when 79 is divided by 8.
7
79 = 8 × 9 + 7, so the remainder is 7.

12 questions · Seed 104731 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

1. Find the remainder when 82 is divided by 7.
82 · 7 · Modular arithmetic & remai…
2. Find the remainder when 143 is divided by 8.
143 · 8 · Modular arithmetic & remai…
3. Find the remainder when 44 is divided by 7.
44 · 7 · Modular arithmetic & remai…
4. Find the remainder when 94 is divided by 5.
94 · 5 · Modular arithmetic & remai…
5. Find the remainder when 76 is divided by 8.
76 · 8 · Modular arithmetic & remai…
6. Find the remainder when 68 is divided by 9.
68 · 9 · Modular arithmetic & remai…
7. Find the remainder when 121 is divided by 7.
121 · 7 · Modular arithmetic & remai…
8. Find the remainder when 123 is divided by 8.
123 · 8 · Modular arithmetic & remai…
9. Find the remainder when 113 is divided by 7.
113 · 7 · Modular arithmetic & remai…
10. Find the remainder when 59 is divided by 7.
59 · 7 · Modular arithmetic & remai…
11. Find the remainder when 188 is divided by 11.
188 · 11 · Modular arithmetic & remai…
12. Find the remainder when 79 is divided by 8.
79 · 8 · Modular arithmetic & remai…

12 questions · Seed 104731 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. Find the remainder when 82 is divided by 7.
5
82 = 7 × 11 + 5, so the remainder is 5.
2. Find the remainder when 143 is divided by 8.
7
143 = 8 × 17 + 7, so the remainder is 7.
3. Find the remainder when 44 is divided by 7.
2
44 = 7 × 6 + 2, so the remainder is 2.
4. Find the remainder when 94 is divided by 5.
4
94 = 5 × 18 + 4, so the remainder is 4.
5. Find the remainder when 76 is divided by 8.
4
76 = 8 × 9 + 4, so the remainder is 4.
6. Find the remainder when 68 is divided by 9.
5
68 = 9 × 7 + 5, so the remainder is 5.
7. Find the remainder when 121 is divided by 7.
2
121 = 7 × 17 + 2, so the remainder is 2.
8. Find the remainder when 123 is divided by 8.
3
123 = 8 × 15 + 3, so the remainder is 3.
9. Find the remainder when 113 is divided by 7.
1
113 = 7 × 16 + 1, so the remainder is 1.
10. Find the remainder when 59 is divided by 7.
3
59 = 7 × 8 + 3, so the remainder is 3.
11. Find the remainder when 188 is divided by 11.
1
188 = 11 × 17 + 1, so the remainder is 1.
12. Find the remainder when 79 is divided by 8.
7
79 = 8 × 9 + 7, so the remainder is 7.

12 questions · Seed 104731 · Age guidance, not curriculum certification