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 108 is divided by 8.
108 · 8 · Modular arithmetic & remai…
2. Find the remainder when 151 is divided by 9.
151 · 9 · Modular arithmetic & remai…
3. Find the remainder when 93 is divided by 11.
93 · 11 · Modular arithmetic & remai…
4. Find the remainder when 153 is divided by 12.
153 · 12 · Modular arithmetic & remai…
5. Find the remainder when 29 is divided by 6.
29 · 6 · Modular arithmetic & remai…
6. Find the remainder when 76 is divided by 8.
76 · 8 · Modular arithmetic & remai…
7. Find the remainder when 167 is divided by 9.
167 · 9 · Modular arithmetic & remai…
8. Find the remainder when 50 is divided by 11.
50 · 11 · Modular arithmetic & remai…
9. Find the remainder when 95 is divided by 7.
95 · 7 · Modular arithmetic & remai…
10. Find the remainder when 69 is divided by 6.
69 · 6 · Modular arithmetic & remai…
11. Find the remainder when 95 is divided by 8.
95 · 8 · Modular arithmetic & remai…
12. Find the remainder when 100 is divided by 9.
100 · 9 · Modular arithmetic & remai…

12 questions · Seed 104735 · 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 108 is divided by 8.
4
108 = 8 × 13 + 4, so the remainder is 4.
2. Find the remainder when 151 is divided by 9.
7
151 = 9 × 16 + 7, so the remainder is 7.
3. Find the remainder when 93 is divided by 11.
5
93 = 11 × 8 + 5, so the remainder is 5.
4. Find the remainder when 153 is divided by 12.
9
153 = 12 × 12 + 9, so the remainder is 9.
5. Find the remainder when 29 is divided by 6.
5
29 = 6 × 4 + 5, so the remainder is 5.
6. Find the remainder when 76 is divided by 8.
4
76 = 8 × 9 + 4, so the remainder is 4.
7. Find the remainder when 167 is divided by 9.
5
167 = 9 × 18 + 5, so the remainder is 5.
8. Find the remainder when 50 is divided by 11.
6
50 = 11 × 4 + 6, so the remainder is 6.
9. Find the remainder when 95 is divided by 7.
4
95 = 7 × 13 + 4, so the remainder is 4.
10. Find the remainder when 69 is divided by 6.
3
69 = 6 × 11 + 3, so the remainder is 3.
11. Find the remainder when 95 is divided by 8.
7
95 = 8 × 11 + 7, so the remainder is 7.
12. Find the remainder when 100 is divided by 9.
1
100 = 9 × 11 + 1, so the remainder is 1.

12 questions · Seed 104735 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

1. Find the remainder when 108 is divided by 8.
108 · 8 · Modular arithmetic & remai…
2. Find the remainder when 151 is divided by 9.
151 · 9 · Modular arithmetic & remai…
3. Find the remainder when 93 is divided by 11.
93 · 11 · Modular arithmetic & remai…
4. Find the remainder when 153 is divided by 12.
153 · 12 · Modular arithmetic & remai…
5. Find the remainder when 29 is divided by 6.
29 · 6 · Modular arithmetic & remai…
6. Find the remainder when 76 is divided by 8.
76 · 8 · Modular arithmetic & remai…
7. Find the remainder when 167 is divided by 9.
167 · 9 · Modular arithmetic & remai…
8. Find the remainder when 50 is divided by 11.
50 · 11 · Modular arithmetic & remai…
9. Find the remainder when 95 is divided by 7.
95 · 7 · Modular arithmetic & remai…
10. Find the remainder when 69 is divided by 6.
69 · 6 · Modular arithmetic & remai…
11. Find the remainder when 95 is divided by 8.
95 · 8 · Modular arithmetic & remai…
12. Find the remainder when 100 is divided by 9.
100 · 9 · Modular arithmetic & remai…

12 questions · Seed 104735 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. Find the remainder when 108 is divided by 8.
4
108 = 8 × 13 + 4, so the remainder is 4.
2. Find the remainder when 151 is divided by 9.
7
151 = 9 × 16 + 7, so the remainder is 7.
3. Find the remainder when 93 is divided by 11.
5
93 = 11 × 8 + 5, so the remainder is 5.
4. Find the remainder when 153 is divided by 12.
9
153 = 12 × 12 + 9, so the remainder is 9.
5. Find the remainder when 29 is divided by 6.
5
29 = 6 × 4 + 5, so the remainder is 5.
6. Find the remainder when 76 is divided by 8.
4
76 = 8 × 9 + 4, so the remainder is 4.
7. Find the remainder when 167 is divided by 9.
5
167 = 9 × 18 + 5, so the remainder is 5.
8. Find the remainder when 50 is divided by 11.
6
50 = 11 × 4 + 6, so the remainder is 6.
9. Find the remainder when 95 is divided by 7.
4
95 = 7 × 13 + 4, so the remainder is 4.
10. Find the remainder when 69 is divided by 6.
3
69 = 6 × 11 + 3, so the remainder is 3.
11. Find the remainder when 95 is divided by 8.
7
95 = 8 × 11 + 7, so the remainder is 7.
12. Find the remainder when 100 is divided by 9.
1
100 = 9 × 11 + 1, so the remainder is 1.

12 questions · Seed 104735 · Age guidance, not curriculum certification