Basic Division

Grade 3 Medium Operations & Algebraic Thinking

Learning Objectives

  • Understand division as sharing equally or forming equal groups
  • Recognize the relationship between multiplication and division

Concept Explanation

Division is the process of splitting a number into equal parts or determining how many equal groups can be formed. For example, 12 ÷ 3 can mean dividing 12 objects into 3 equal groups (with 4 in each group) or forming groups of 3 until all 12 objects are used (making 4 groups).

Division is closely related to multiplication—it’s the inverse operation. If 3 × 4 = 12, then 12 ÷ 3 = 4 and 12 ÷ 4 = 3.

Worked Examples

Example 1

Problem: 8 ÷ 2
Solution: 4
Explanation: 8 can be divided into 2 equal groups with 4 in each group.

Example 2

Problem: 15 ÷ 3
Solution: 5
Explanation: 15 objects can be arranged into 5 groups of 3, or 3 groups of 5.

Example 3

Problem: 20 ÷ 4
Solution: 5
Explanation: 20 divided into 4 equal parts gives 5 in each part.

Common Errors

ErrorCorrectionReason
Confusing dividend and divisorRemember the first number is being dividedIn 12 ÷ 3, 12 is the dividend (being divided) and 3 is the divisor.
Forgetting the relationship with multiplicationUse multiplication facts to help with divisionIf you know 7 × 8 = 56, then 56 ÷ 8 = 7.
Incorrect interpretation of remaindersUnderstand what the remainder representsIn 17 ÷ 5 = 3 remainder 2, the 2 represents objects that couldn’t form a complete group.

Practice Problems

  1. Problem: 10 ÷ 2
    Solution: 5
  2. Problem: 18 ÷ 3
    Solution: 6
  3. Problem: 24 ÷ 6
    Solution: 4
  4. Problem: 16 ÷ 4
    Solution: 4
  5. Problem: 25 ÷ 5
    Solution: 5

Real-World Application Example

Division is used in many everyday situations, such as sharing food equally among friends, determining how many teams can be formed from a group of students, or calculating how many miles per gallon a car gets. Understanding division helps with fair distribution of resources and efficient planning.

Related Concepts