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 61 is divided by 6.
61 · 6 · Modular arithmetic & remai…
2. Find the remainder when 217 is divided by 12.
217 · 12 · Modular arithmetic & remai…
3. Find the remainder when 203 is divided by 11.
203 · 11 · Modular arithmetic & remai…
4. Find the remainder when 127 is divided by 7.
127 · 7 · Modular arithmetic & remai…
5. Find the remainder when 166 is divided by 11.
166 · 11 · Modular arithmetic & remai…
6. Find the remainder when 129 is divided by 12.
129 · 12 · Modular arithmetic & remai…
7. Find the remainder when 19 is divided by 6.
19 · 6 · Modular arithmetic & remai…
8. Find the remainder when 92 is divided by 7.
92 · 7 · Modular arithmetic & remai…
9. Find the remainder when 200 is divided by 12.
200 · 12 · Modular arithmetic & remai…
10. Find the remainder when 152 is divided by 9.
152 · 9 · Modular arithmetic & remai…
11. Find the remainder when 142 is divided by 8.
142 · 8 · Modular arithmetic & remai…
12. Find the remainder when 177 is divided by 12.
177 · 12 · Modular arithmetic & remai…

12 questions · Seed 104737 · 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 61 is divided by 6.
1
61 = 6 × 10 + 1, so the remainder is 1.
2. Find the remainder when 217 is divided by 12.
1
217 = 12 × 18 + 1, so the remainder is 1.
3. Find the remainder when 203 is divided by 11.
5
203 = 11 × 18 + 5, so the remainder is 5.
4. Find the remainder when 127 is divided by 7.
1
127 = 7 × 18 + 1, so the remainder is 1.
5. Find the remainder when 166 is divided by 11.
1
166 = 11 × 15 + 1, so the remainder is 1.
6. Find the remainder when 129 is divided by 12.
9
129 = 12 × 10 + 9, so the remainder is 9.
7. Find the remainder when 19 is divided by 6.
1
19 = 6 × 3 + 1, so the remainder is 1.
8. Find the remainder when 92 is divided by 7.
1
92 = 7 × 13 + 1, so the remainder is 1.
9. Find the remainder when 200 is divided by 12.
8
200 = 12 × 16 + 8, so the remainder is 8.
10. Find the remainder when 152 is divided by 9.
8
152 = 9 × 16 + 8, so the remainder is 8.
11. Find the remainder when 142 is divided by 8.
6
142 = 8 × 17 + 6, so the remainder is 6.
12. Find the remainder when 177 is divided by 12.
9
177 = 12 × 14 + 9, so the remainder is 9.

12 questions · Seed 104737 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

1. Find the remainder when 61 is divided by 6.
61 · 6 · Modular arithmetic & remai…
2. Find the remainder when 217 is divided by 12.
217 · 12 · Modular arithmetic & remai…
3. Find the remainder when 203 is divided by 11.
203 · 11 · Modular arithmetic & remai…
4. Find the remainder when 127 is divided by 7.
127 · 7 · Modular arithmetic & remai…
5. Find the remainder when 166 is divided by 11.
166 · 11 · Modular arithmetic & remai…
6. Find the remainder when 129 is divided by 12.
129 · 12 · Modular arithmetic & remai…
7. Find the remainder when 19 is divided by 6.
19 · 6 · Modular arithmetic & remai…
8. Find the remainder when 92 is divided by 7.
92 · 7 · Modular arithmetic & remai…
9. Find the remainder when 200 is divided by 12.
200 · 12 · Modular arithmetic & remai…
10. Find the remainder when 152 is divided by 9.
152 · 9 · Modular arithmetic & remai…
11. Find the remainder when 142 is divided by 8.
142 · 8 · Modular arithmetic & remai…
12. Find the remainder when 177 is divided by 12.
177 · 12 · Modular arithmetic & remai…

12 questions · Seed 104737 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. Find the remainder when 61 is divided by 6.
1
61 = 6 × 10 + 1, so the remainder is 1.
2. Find the remainder when 217 is divided by 12.
1
217 = 12 × 18 + 1, so the remainder is 1.
3. Find the remainder when 203 is divided by 11.
5
203 = 11 × 18 + 5, so the remainder is 5.
4. Find the remainder when 127 is divided by 7.
1
127 = 7 × 18 + 1, so the remainder is 1.
5. Find the remainder when 166 is divided by 11.
1
166 = 11 × 15 + 1, so the remainder is 1.
6. Find the remainder when 129 is divided by 12.
9
129 = 12 × 10 + 9, so the remainder is 9.
7. Find the remainder when 19 is divided by 6.
1
19 = 6 × 3 + 1, so the remainder is 1.
8. Find the remainder when 92 is divided by 7.
1
92 = 7 × 13 + 1, so the remainder is 1.
9. Find the remainder when 200 is divided by 12.
8
200 = 12 × 16 + 8, so the remainder is 8.
10. Find the remainder when 152 is divided by 9.
8
152 = 9 × 16 + 8, so the remainder is 8.
11. Find the remainder when 142 is divided by 8.
6
142 = 8 × 17 + 6, so the remainder is 6.
12. Find the remainder when 177 is divided by 12.
9
177 = 12 × 14 + 9, so the remainder is 9.

12 questions · Seed 104737 · Age guidance, not curriculum certification