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 58 is divided by 9.
58 · 9 · Modular arithmetic & remai…
2. Find the remainder when 97 is divided by 7.
97 · 7 · Modular arithmetic & remai…
3. Find the remainder when 20 is divided by 6.
20 · 6 · Modular arithmetic & remai…
4. Find the remainder when 131 is divided by 12.
131 · 12 · Modular arithmetic & remai…
5. Find the remainder when 59 is divided by 12.
59 · 12 · Modular arithmetic & remai…
6. Find the remainder when 159 is divided by 12.
159 · 12 · Modular arithmetic & remai…
7. Find the remainder when 115 is divided by 8.
115 · 8 · Modular arithmetic & remai…
8. Find the remainder when 36 is divided by 5.
36 · 5 · Modular arithmetic & remai…
9. Find the remainder when 57 is divided by 9.
57 · 9 · Modular arithmetic & remai…
10. Find the remainder when 76 is divided by 7.
76 · 7 · Modular arithmetic & remai…
11. Find the remainder when 49 is divided by 6.
49 · 6 · Modular arithmetic & remai…
12. Find the remainder when 27 is divided by 7.
27 · 7 · Modular arithmetic & remai…

12 questions · Seed 104738 · 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 58 is divided by 9.
4
58 = 9 × 6 + 4, so the remainder is 4.
2. Find the remainder when 97 is divided by 7.
6
97 = 7 × 13 + 6, so the remainder is 6.
3. Find the remainder when 20 is divided by 6.
2
20 = 6 × 3 + 2, so the remainder is 2.
4. Find the remainder when 131 is divided by 12.
11
131 = 12 × 10 + 11, so the remainder is 11.
5. Find the remainder when 59 is divided by 12.
11
59 = 12 × 4 + 11, so the remainder is 11.
6. Find the remainder when 159 is divided by 12.
3
159 = 12 × 13 + 3, so the remainder is 3.
7. Find the remainder when 115 is divided by 8.
3
115 = 8 × 14 + 3, so the remainder is 3.
8. Find the remainder when 36 is divided by 5.
1
36 = 5 × 7 + 1, so the remainder is 1.
9. Find the remainder when 57 is divided by 9.
3
57 = 9 × 6 + 3, so the remainder is 3.
10. Find the remainder when 76 is divided by 7.
6
76 = 7 × 10 + 6, so the remainder is 6.
11. Find the remainder when 49 is divided by 6.
1
49 = 6 × 8 + 1, so the remainder is 1.
12. Find the remainder when 27 is divided by 7.
6
27 = 7 × 3 + 6, so the remainder is 6.

12 questions · Seed 104738 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

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 97 is divided by 7.
97 · 7 · Modular arithmetic & remai…
3. Find the remainder when 20 is divided by 6.
20 · 6 · Modular arithmetic & remai…
4. Find the remainder when 131 is divided by 12.
131 · 12 · Modular arithmetic & remai…
5. Find the remainder when 59 is divided by 12.
59 · 12 · Modular arithmetic & remai…
6. Find the remainder when 159 is divided by 12.
159 · 12 · Modular arithmetic & remai…
7. Find the remainder when 115 is divided by 8.
115 · 8 · Modular arithmetic & remai…
8. Find the remainder when 36 is divided by 5.
36 · 5 · Modular arithmetic & remai…
9. Find the remainder when 57 is divided by 9.
57 · 9 · Modular arithmetic & remai…
10. Find the remainder when 76 is divided by 7.
76 · 7 · Modular arithmetic & remai…
11. Find the remainder when 49 is divided by 6.
49 · 6 · Modular arithmetic & remai…
12. Find the remainder when 27 is divided by 7.
27 · 7 · Modular arithmetic & remai…

12 questions · Seed 104738 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

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 97 is divided by 7.
6
97 = 7 × 13 + 6, so the remainder is 6.
3. Find the remainder when 20 is divided by 6.
2
20 = 6 × 3 + 2, so the remainder is 2.
4. Find the remainder when 131 is divided by 12.
11
131 = 12 × 10 + 11, so the remainder is 11.
5. Find the remainder when 59 is divided by 12.
11
59 = 12 × 4 + 11, so the remainder is 11.
6. Find the remainder when 159 is divided by 12.
3
159 = 12 × 13 + 3, so the remainder is 3.
7. Find the remainder when 115 is divided by 8.
3
115 = 8 × 14 + 3, so the remainder is 3.
8. Find the remainder when 36 is divided by 5.
1
36 = 5 × 7 + 1, so the remainder is 1.
9. Find the remainder when 57 is divided by 9.
3
57 = 9 × 6 + 3, so the remainder is 3.
10. Find the remainder when 76 is divided by 7.
6
76 = 7 × 10 + 6, so the remainder is 6.
11. Find the remainder when 49 is divided by 6.
1
49 = 6 × 8 + 1, so the remainder is 1.
12. Find the remainder when 27 is divided by 7.
6
27 = 7 × 3 + 6, so the remainder is 6.

12 questions · Seed 104738 · Age guidance, not curriculum certification