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 97 is divided by 8.
97 · 8 · Modular arithmetic & remai…
2. Find the remainder when 140 is divided by 11.
140 · 11 · Modular arithmetic & remai…
3. Find the remainder when 80 is divided by 7.
80 · 7 · Modular arithmetic & remai…
4. Find the remainder when 73 is divided by 7.
73 · 7 · Modular arithmetic & remai…
5. Find the remainder when 113 is divided by 8.
113 · 8 · Modular arithmetic & remai…
6. Find the remainder when 152 is divided by 9.
152 · 9 · Modular arithmetic & remai…
7. Find the remainder when 74 is divided by 7.
74 · 7 · Modular arithmetic & remai…
8. Find the remainder when 82 is divided by 7.
82 · 7 · Modular arithmetic & remai…
9. Find the remainder when 56 is divided by 9.
56 · 9 · Modular arithmetic & remai…
10. Find the remainder when 177 is divided by 12.
177 · 12 · Modular arithmetic & remai…
11. Find the remainder when 65 is divided by 8.
65 · 8 · Modular arithmetic & remai…
12. Find the remainder when 96 is divided by 9.
96 · 9 · Modular arithmetic & remai…

12 questions · Seed 104729 · 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 97 is divided by 8.
1
97 = 8 × 12 + 1, so the remainder is 1.
2. Find the remainder when 140 is divided by 11.
8
140 = 11 × 12 + 8, so the remainder is 8.
3. Find the remainder when 80 is divided by 7.
3
80 = 7 × 11 + 3, so the remainder is 3.
4. Find the remainder when 73 is divided by 7.
3
73 = 7 × 10 + 3, so the remainder is 3.
5. Find the remainder when 113 is divided by 8.
1
113 = 8 × 14 + 1, so the remainder is 1.
6. Find the remainder when 152 is divided by 9.
8
152 = 9 × 16 + 8, so the remainder is 8.
7. Find the remainder when 74 is divided by 7.
4
74 = 7 × 10 + 4, so the remainder is 4.
8. Find the remainder when 82 is divided by 7.
5
82 = 7 × 11 + 5, so the remainder is 5.
9. Find the remainder when 56 is divided by 9.
2
56 = 9 × 6 + 2, so the remainder is 2.
10. Find the remainder when 177 is divided by 12.
9
177 = 12 × 14 + 9, so the remainder is 9.
11. Find the remainder when 65 is divided by 8.
1
65 = 8 × 8 + 1, so the remainder is 1.
12. Find the remainder when 96 is divided by 9.
6
96 = 9 × 10 + 6, so the remainder is 6.

12 questions · Seed 104729 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Take your time. Show your thinking.

1. Find the remainder when 97 is divided by 8.
97 · 8 · Modular arithmetic & remai…
2. Find the remainder when 140 is divided by 11.
140 · 11 · Modular arithmetic & remai…
3. Find the remainder when 80 is divided by 7.
80 · 7 · Modular arithmetic & remai…
4. Find the remainder when 73 is divided by 7.
73 · 7 · Modular arithmetic & remai…
5. Find the remainder when 113 is divided by 8.
113 · 8 · Modular arithmetic & remai…
6. Find the remainder when 152 is divided by 9.
152 · 9 · Modular arithmetic & remai…
7. Find the remainder when 74 is divided by 7.
74 · 7 · Modular arithmetic & remai…
8. Find the remainder when 82 is divided by 7.
82 · 7 · Modular arithmetic & remai…
9. Find the remainder when 56 is divided by 9.
56 · 9 · Modular arithmetic & remai…
10. Find the remainder when 177 is divided by 12.
177 · 12 · Modular arithmetic & remai…
11. Find the remainder when 65 is divided by 8.
65 · 8 · Modular arithmetic & remai…
12. Find the remainder when 96 is divided by 9.
96 · 9 · Modular arithmetic & remai…

12 questions · Seed 104729 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Answers and reasoning. Review before teaching.

1. Find the remainder when 97 is divided by 8.
1
97 = 8 × 12 + 1, so the remainder is 1.
2. Find the remainder when 140 is divided by 11.
8
140 = 11 × 12 + 8, so the remainder is 8.
3. Find the remainder when 80 is divided by 7.
3
80 = 7 × 11 + 3, so the remainder is 3.
4. Find the remainder when 73 is divided by 7.
3
73 = 7 × 10 + 3, so the remainder is 3.
5. Find the remainder when 113 is divided by 8.
1
113 = 8 × 14 + 1, so the remainder is 1.
6. Find the remainder when 152 is divided by 9.
8
152 = 9 × 16 + 8, so the remainder is 8.
7. Find the remainder when 74 is divided by 7.
4
74 = 7 × 10 + 4, so the remainder is 4.
8. Find the remainder when 82 is divided by 7.
5
82 = 7 × 11 + 5, so the remainder is 5.
9. Find the remainder when 56 is divided by 9.
2
56 = 9 × 6 + 2, so the remainder is 2.
10. Find the remainder when 177 is divided by 12.
9
177 = 12 × 14 + 9, so the remainder is 9.
11. Find the remainder when 65 is divided by 8.
1
65 = 8 × 8 + 1, so the remainder is 1.
12. Find the remainder when 96 is divided by 9.
6
96 = 9 × 10 + 6, so the remainder is 6.

12 questions · Seed 104729 · Age guidance, not curriculum certification