Skip to content

Exercises: Quotients and Remainders

Exercise 1: Basic Division and Remainders

  1. \( 27 \div 5 \) Quotient: 5 Remainder: 2

  2. \( 42 \div 8 \) Quotient: 5 Remainder: 2

  3. \( 100 \div 6 \) Quotient: 16 Remainder: 4

Exercise 2: Modulus Operations

  1. \( 27 \mod 5 \) Result: 2

  2. \( 42 \mod 8 \) Result: 2

  3. \( 100 \mod 6 \) Result: 4

Exercise 3: Word Problems

  1. A teacher has 45 pencils and wants to distribute them evenly among 6 students.
  2. Pencils per student: \( 45 \div 6 = 7 \)

  3. Leftover pencils: \( 45 - (6 \times 7) = 3 \) Answer: Each student receives 7 pencils, and 3 pencils are left over.

  4. A baker has 120 cookies to pack into boxes that hold 12 cookies each.

  5. Full boxes: \( 120 \div 12 = 10 \)

  6. Leftover cookies: \( 120 - (10 \times 12) = 0 \) Answer: 10 full boxes can be filled, and there are 0 cookies left.

  7. A farmer has 250 apples to put into bags of 10.

  8. Full bags: \( 250 \div 10 = 25 \)
  9. Remaining apples: \( 250 - (25 \times 10) = 0 \) Answer: 25 full bags can be made, and there are 0 apples remaining.

Exercise 4: Find the Quotient and Remainder

  1. \( 63 \div 4 \) Quotient: 15 Remainder: 3 Expressed as: \( 63 = 4 \cdot 15 + 3 \)

  2. \( 88 \div 7 \) Quotient: 12 Remainder: 4 Expressed as: \( 88 = 7 \cdot 12 + 4 \)

  3. \( 150 \div 9 \) Quotient: 16 Remainder: 6 Expressed as: \( 150 = 9 \cdot 16 + 6 \)

Exercise 5: Mixed Operations

  1. \( 56 + 35 \div 5 \) First, calculate \( 35 \div 5 = 7 \) \( 56 + 7 = 63 \) Quotient: 63, Remainder: 0

  2. \( 90 - 14 \div 2 \) First, calculate \( 14 \div 2 = 7 \) \( 90 - 7 = 83 \) Quotient: 83, Remainder: 0

  3. \( 120 \div (3 + 3) \) First, calculate \( 3 + 3 = 6 \) \( 120 \div 6 = 20 \) Quotient: 20, Remainder: 0

Exercise 6: Advanced Division and Modulus

  1. \( 987 \div 34 \) Quotient: 29 Remainder: 1 \( 987 \mod 34 = 1 \)

  2. \( 1456 \div 23 \) Quotient: 63 Remainder: 7 \( 1456 \mod 23 = 7 \)

  3. \( 3021 \div 15 \) Quotient: 201 Remainder: 6 \( 3021 \mod 15 = 6 \)

Exercise 7: Additional Modulus Operations

  1. \( 58 \mod 7 \) Result: 2

  2. \( 125 \mod 11 \) Result: 4

  3. \( 320 \mod 13 \) Result: 1