ReasoningAges 13-15

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 13-15

Take your time. Show your thinking.

1. Find the remainder when 17 is divided by 5.
17 · 5 · Modular arithmetic & remai…
2. Find the remainder when 132 is divided by 7.
132 · 7 · Modular arithmetic & remai…
3. Find the remainder when 29 is divided by 6.
29 · 6 · Modular arithmetic & remai…
4. Find the remainder when 144 is divided by 11.
144 · 11 · Modular arithmetic & remai…
5. Find the remainder when 156 is divided by 11.
156 · 11 · Modular arithmetic & remai…
6. Find the remainder when 175 is divided by 12.
175 · 12 · Modular arithmetic & remai…
7. Find the remainder when 111 is divided by 11.
111 · 11 · Modular arithmetic & remai…
8. Find the remainder when 105 is divided by 11.
105 · 11 · Modular arithmetic & remai…
9. Find the remainder when 87 is divided by 5.
87 · 5 · Modular arithmetic & remai…
10. Find the remainder when 71 is divided by 7.
71 · 7 · Modular arithmetic & remai…
11. Find the remainder when 168 is divided by 9.
168 · 9 · Modular arithmetic & remai…
12. Find the remainder when 50 is divided by 8.
50 · 8 · Modular arithmetic & remai…

12 questions · Seed 48 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Answers and reasoning. Review before teaching.

1. Find the remainder when 17 is divided by 5.
2
17 = 5 × 3 + 2, so the remainder is 2.
2. Find the remainder when 132 is divided by 7.
6
132 = 7 × 18 + 6, so the remainder is 6.
3. Find the remainder when 29 is divided by 6.
5
29 = 6 × 4 + 5, so the remainder is 5.
4. Find the remainder when 144 is divided by 11.
1
144 = 11 × 13 + 1, so the remainder is 1.
5. Find the remainder when 156 is divided by 11.
2
156 = 11 × 14 + 2, so the remainder is 2.
6. Find the remainder when 175 is divided by 12.
7
175 = 12 × 14 + 7, so the remainder is 7.
7. Find the remainder when 111 is divided by 11.
1
111 = 11 × 10 + 1, so the remainder is 1.
8. Find the remainder when 105 is divided by 11.
6
105 = 11 × 9 + 6, so the remainder is 6.
9. Find the remainder when 87 is divided by 5.
2
87 = 5 × 17 + 2, so the remainder is 2.
10. Find the remainder when 71 is divided by 7.
1
71 = 7 × 10 + 1, so the remainder is 1.
11. Find the remainder when 168 is divided by 9.
6
168 = 9 × 18 + 6, so the remainder is 6.
12. Find the remainder when 50 is divided by 8.
2
50 = 8 × 6 + 2, so the remainder is 2.

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Take your time. Show your thinking.

1. Find the remainder when 17 is divided by 5.
17 · 5 · Modular arithmetic & remai…
2. Find the remainder when 132 is divided by 7.
132 · 7 · Modular arithmetic & remai…
3. Find the remainder when 29 is divided by 6.
29 · 6 · Modular arithmetic & remai…
4. Find the remainder when 144 is divided by 11.
144 · 11 · Modular arithmetic & remai…
5. Find the remainder when 156 is divided by 11.
156 · 11 · Modular arithmetic & remai…
6. Find the remainder when 175 is divided by 12.
175 · 12 · Modular arithmetic & remai…
7. Find the remainder when 111 is divided by 11.
111 · 11 · Modular arithmetic & remai…
8. Find the remainder when 105 is divided by 11.
105 · 11 · Modular arithmetic & remai…
9. Find the remainder when 87 is divided by 5.
87 · 5 · Modular arithmetic & remai…
10. Find the remainder when 71 is divided by 7.
71 · 7 · Modular arithmetic & remai…
11. Find the remainder when 168 is divided by 9.
168 · 9 · Modular arithmetic & remai…
12. Find the remainder when 50 is divided by 8.
50 · 8 · Modular arithmetic & remai…

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Answers and reasoning. Review before teaching.

1. Find the remainder when 17 is divided by 5.
2
17 = 5 × 3 + 2, so the remainder is 2.
2. Find the remainder when 132 is divided by 7.
6
132 = 7 × 18 + 6, so the remainder is 6.
3. Find the remainder when 29 is divided by 6.
5
29 = 6 × 4 + 5, so the remainder is 5.
4. Find the remainder when 144 is divided by 11.
1
144 = 11 × 13 + 1, so the remainder is 1.
5. Find the remainder when 156 is divided by 11.
2
156 = 11 × 14 + 2, so the remainder is 2.
6. Find the remainder when 175 is divided by 12.
7
175 = 12 × 14 + 7, so the remainder is 7.
7. Find the remainder when 111 is divided by 11.
1
111 = 11 × 10 + 1, so the remainder is 1.
8. Find the remainder when 105 is divided by 11.
6
105 = 11 × 9 + 6, so the remainder is 6.
9. Find the remainder when 87 is divided by 5.
2
87 = 5 × 17 + 2, so the remainder is 2.
10. Find the remainder when 71 is divided by 7.
1
71 = 7 × 10 + 1, so the remainder is 1.
11. Find the remainder when 168 is divided by 9.
6
168 = 9 × 18 + 6, so the remainder is 6.
12. Find the remainder when 50 is divided by 8.
2
50 = 8 × 6 + 2, so the remainder is 2.

12 questions · Seed 48 · Age guidance, not curriculum certification