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 58 is divided by 9.
58 · 9 · Modular arithmetic & remai…
2. Find the remainder when 151 is divided by 12.
151 · 12 · Modular arithmetic & remai…
3. Find the remainder when 129 is divided by 9.
129 · 9 · Modular arithmetic & remai…
4. Find the remainder when 56 is divided by 5.
56 · 5 · Modular arithmetic & remai…
5. Find the remainder when 56 is divided by 12.
56 · 12 · Modular arithmetic & remai…
6. Find the remainder when 53 is divided by 9.
53 · 9 · Modular arithmetic & remai…
7. Find the remainder when 85 is divided by 7.
85 · 7 · Modular arithmetic & remai…
8. Find the remainder when 35 is divided by 6.
35 · 6 · Modular arithmetic & remai…
9. Find the remainder when 42 is divided by 12.
42 · 12 · Modular arithmetic & remai…
10. Find the remainder when 121 is divided by 8.
121 · 8 · Modular arithmetic & remai…
11. Find the remainder when 163 is divided by 11.
163 · 11 · Modular arithmetic & remai…
12. Find the remainder when 71 is divided by 7.
71 · 7 · Modular arithmetic & remai…

12 questions · Seed 104733 · 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 58 is divided by 9.
4
58 = 9 × 6 + 4, so the remainder is 4.
2. Find the remainder when 151 is divided by 12.
7
151 = 12 × 12 + 7, so the remainder is 7.
3. Find the remainder when 129 is divided by 9.
3
129 = 9 × 14 + 3, so the remainder is 3.
4. Find the remainder when 56 is divided by 5.
1
56 = 5 × 11 + 1, so the remainder is 1.
5. Find the remainder when 56 is divided by 12.
8
56 = 12 × 4 + 8, so the remainder is 8.
6. Find the remainder when 53 is divided by 9.
8
53 = 9 × 5 + 8, so the remainder is 8.
7. Find the remainder when 85 is divided by 7.
1
85 = 7 × 12 + 1, so the remainder is 1.
8. Find the remainder when 35 is divided by 6.
5
35 = 6 × 5 + 5, so the remainder is 5.
9. Find the remainder when 42 is divided by 12.
6
42 = 12 × 3 + 6, so the remainder is 6.
10. Find the remainder when 121 is divided by 8.
1
121 = 8 × 15 + 1, so the remainder is 1.
11. Find the remainder when 163 is divided by 11.
9
163 = 11 × 14 + 9, so the remainder is 9.
12. Find the remainder when 71 is divided by 7.
1
71 = 7 × 10 + 1, so the remainder is 1.

12 questions · Seed 104733 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

1. Find the remainder when 58 is divided by 9.
58 · 9 · Modular arithmetic & remai…
2. Find the remainder when 151 is divided by 12.
151 · 12 · Modular arithmetic & remai…
3. Find the remainder when 129 is divided by 9.
129 · 9 · Modular arithmetic & remai…
4. Find the remainder when 56 is divided by 5.
56 · 5 · Modular arithmetic & remai…
5. Find the remainder when 56 is divided by 12.
56 · 12 · Modular arithmetic & remai…
6. Find the remainder when 53 is divided by 9.
53 · 9 · Modular arithmetic & remai…
7. Find the remainder when 85 is divided by 7.
85 · 7 · Modular arithmetic & remai…
8. Find the remainder when 35 is divided by 6.
35 · 6 · Modular arithmetic & remai…
9. Find the remainder when 42 is divided by 12.
42 · 12 · Modular arithmetic & remai…
10. Find the remainder when 121 is divided by 8.
121 · 8 · Modular arithmetic & remai…
11. Find the remainder when 163 is divided by 11.
163 · 11 · Modular arithmetic & remai…
12. Find the remainder when 71 is divided by 7.
71 · 7 · Modular arithmetic & remai…

12 questions · Seed 104733 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. Find the remainder when 58 is divided by 9.
4
58 = 9 × 6 + 4, so the remainder is 4.
2. Find the remainder when 151 is divided by 12.
7
151 = 12 × 12 + 7, so the remainder is 7.
3. Find the remainder when 129 is divided by 9.
3
129 = 9 × 14 + 3, so the remainder is 3.
4. Find the remainder when 56 is divided by 5.
1
56 = 5 × 11 + 1, so the remainder is 1.
5. Find the remainder when 56 is divided by 12.
8
56 = 12 × 4 + 8, so the remainder is 8.
6. Find the remainder when 53 is divided by 9.
8
53 = 9 × 5 + 8, so the remainder is 8.
7. Find the remainder when 85 is divided by 7.
1
85 = 7 × 12 + 1, so the remainder is 1.
8. Find the remainder when 35 is divided by 6.
5
35 = 6 × 5 + 5, so the remainder is 5.
9. Find the remainder when 42 is divided by 12.
6
42 = 12 × 3 + 6, so the remainder is 6.
10. Find the remainder when 121 is divided by 8.
1
121 = 8 × 15 + 1, so the remainder is 1.
11. Find the remainder when 163 is divided by 11.
9
163 = 11 × 14 + 9, so the remainder is 9.
12. Find the remainder when 71 is divided by 7.
1
71 = 7 × 10 + 1, so the remainder is 1.

12 questions · Seed 104733 · Age guidance, not curriculum certification