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 86 is divided by 5.
86 · 5 · Modular arithmetic & remai…
3. Find the remainder when 94 is divided by 7.
94 · 7 · Modular arithmetic & remai…
4. Find the remainder when 73 is divided by 5.
73 · 5 · Modular arithmetic & remai…
5. Find the remainder when 64 is divided by 7.
64 · 7 · Modular arithmetic & remai…
6. Find the remainder when 93 is divided by 11.
93 · 11 · Modular arithmetic & remai…
7. Find the remainder when 26 is divided by 7.
26 · 7 · Modular arithmetic & remai…
8. Find the remainder when 64 is divided by 5.
64 · 5 · Modular arithmetic & remai…
9. Find the remainder when 137 is divided by 8.
137 · 8 · Modular arithmetic & remai…
10. Find the remainder when 113 is divided by 6.
113 · 6 · Modular arithmetic & remai…
11. Find the remainder when 36 is divided by 5.
36 · 5 · Modular arithmetic & remai…
12. Find the remainder when 79 is divided by 8.
79 · 8 · Modular arithmetic & remai…

12 questions · Seed 104740 · 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 86 is divided by 5.
1
86 = 5 × 17 + 1, so the remainder is 1.
3. Find the remainder when 94 is divided by 7.
3
94 = 7 × 13 + 3, so the remainder is 3.
4. Find the remainder when 73 is divided by 5.
3
73 = 5 × 14 + 3, so the remainder is 3.
5. Find the remainder when 64 is divided by 7.
1
64 = 7 × 9 + 1, so the remainder is 1.
6. Find the remainder when 93 is divided by 11.
5
93 = 11 × 8 + 5, so the remainder is 5.
7. Find the remainder when 26 is divided by 7.
5
26 = 7 × 3 + 5, so the remainder is 5.
8. Find the remainder when 64 is divided by 5.
4
64 = 5 × 12 + 4, so the remainder is 4.
9. Find the remainder when 137 is divided by 8.
1
137 = 8 × 17 + 1, so the remainder is 1.
10. Find the remainder when 113 is divided by 6.
5
113 = 6 × 18 + 5, so the remainder is 5.
11. Find the remainder when 36 is divided by 5.
1
36 = 5 × 7 + 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 104740 · 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 86 is divided by 5.
86 · 5 · Modular arithmetic & remai…
3. Find the remainder when 94 is divided by 7.
94 · 7 · Modular arithmetic & remai…
4. Find the remainder when 73 is divided by 5.
73 · 5 · Modular arithmetic & remai…
5. Find the remainder when 64 is divided by 7.
64 · 7 · Modular arithmetic & remai…
6. Find the remainder when 93 is divided by 11.
93 · 11 · Modular arithmetic & remai…
7. Find the remainder when 26 is divided by 7.
26 · 7 · Modular arithmetic & remai…
8. Find the remainder when 64 is divided by 5.
64 · 5 · Modular arithmetic & remai…
9. Find the remainder when 137 is divided by 8.
137 · 8 · Modular arithmetic & remai…
10. Find the remainder when 113 is divided by 6.
113 · 6 · Modular arithmetic & remai…
11. Find the remainder when 36 is divided by 5.
36 · 5 · Modular arithmetic & remai…
12. Find the remainder when 79 is divided by 8.
79 · 8 · Modular arithmetic & remai…

12 questions · Seed 104740 · 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 86 is divided by 5.
1
86 = 5 × 17 + 1, so the remainder is 1.
3. Find the remainder when 94 is divided by 7.
3
94 = 7 × 13 + 3, so the remainder is 3.
4. Find the remainder when 73 is divided by 5.
3
73 = 5 × 14 + 3, so the remainder is 3.
5. Find the remainder when 64 is divided by 7.
1
64 = 7 × 9 + 1, so the remainder is 1.
6. Find the remainder when 93 is divided by 11.
5
93 = 11 × 8 + 5, so the remainder is 5.
7. Find the remainder when 26 is divided by 7.
5
26 = 7 × 3 + 5, so the remainder is 5.
8. Find the remainder when 64 is divided by 5.
4
64 = 5 × 12 + 4, so the remainder is 4.
9. Find the remainder when 137 is divided by 8.
1
137 = 8 × 17 + 1, so the remainder is 1.
10. Find the remainder when 113 is divided by 6.
5
113 = 6 × 18 + 5, so the remainder is 5.
11. Find the remainder when 36 is divided by 5.
1
36 = 5 × 7 + 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 104740 · Age guidance, not curriculum certification