Table of Contents

Using an efficient method for division Level 4

Introduction

Have you ever tried to share a large pizza among your friends? Dividing it evenly can be tricky, especially if there are many slices! Learning an efficient method for division helps us tackle bigger numbers and share things fairly. In this article, we will explore how to divide numbers effectively, making math easier and more enjoyable.

Definition and Concept

Division is one of the four basic operations in mathematics, along with addition, subtraction, and multiplication. It involves splitting a number (the dividend) into equal parts (the divisor) to find out how many times the divisor fits into the dividend.

For example: In the expression 20 ÷ 4, 20 is the dividend, 4 is the divisor, and the result (5) tells us how many groups of 4 can be made from 20.

Relevance:

  • Mathematics: Division is essential for understanding fractions, ratios, and proportions.
  • Real-world applications: Used in budgeting, cooking, sharing, and problem-solving scenarios.

Historical Context or Origin​

The concept of division dates back to ancient civilizations, including the Babylonians and Egyptians, who used it for trade and resource allocation. The long division method we use today was developed over centuries, with significant contributions from mathematicians in the Middle Ages.

Understanding the Problem

To solve a division problem efficiently, we need to understand the relationship between the dividend, divisor, and quotient. Let’s break this down with an example:
Example Problem: 144 ÷ 12

  • Identify the dividend (144) and the divisor (12).
  • Determine how many times 12 fits into 144.

    • Methods to Solve the Problem with different types of problems​

    Method 1: Long Division

  • Write the dividend inside the division bracket and the divisor outside.
  • Estimate how many times the divisor fits into the leading digits of the dividend.
  • Multiply and subtract, bringing down the next digit if necessary.
  • Repeat until all digits have been used.

    • Example:
    Solve 144 ÷ 12 using long division.

  • 12 goes into 14 once (1). Multiply 1 × 12 = 12. Subtract: 14 – 12 = 2. Bring down the 4 to make 24.
  • 12 goes into 24 exactly 2 times (2). Multiply 2 × 12 = 24. Subtract: 24 – 24 = 0.
  • The answer is 12.

    • Method 2: Using Multiplication Facts

  • Think of division as the reverse of multiplication.
  • Use known multiplication tables to find the quotient.

    • Example:
    Solve 56 ÷ 7.

  • Recall that 7 × 8 = 56, so the answer is 8.

    • Method 3: Estimation

  • Round the numbers to make them easier to divide.
  • Estimate the quotient and then adjust if necessary.

    • Example:
    Solve 198 ÷ 9.

  • Round 198 to 200. Estimate: 200 ÷ 10 = 20. Check: 9 × 22 = 198, so the exact answer is 22.

    • Exceptions and Special Cases​

  • Division by Zero: Dividing any number by zero is undefined. For example, 5 ÷ 0 has no answer.
  • Remainders: Sometimes, division does not result in a whole number. For example, 10 ÷ 3 = 3 with a remainder of 1.

    • Step-by-Step Practice​

    Problem 1: Solve 84 ÷ 7.

    Solution:

  • 7 goes into 8 once (1). Multiply: 1 × 7 = 7. Subtract: 8 – 7 = 1. Bring down the 4 to make 14.
  • 7 goes into 14 exactly 2 times (2). Multiply: 2 × 7 = 14. Subtract: 14 – 14 = 0.
  • The answer is 12.

    • Problem 2: Solve 56 ÷ 8.

    Solution:

    1. Using multiplication facts: 8 × 7 = 56.
    2. The answer is 7.

    Examples and Variations

    Easy Example:

    • Problem: Solve 36 ÷ 6
    • Solution: 6 goes into 36 exactly 6 times. The answer is 6.

    Moderate Example:

    • Problem: Solve 144 ÷ 12
    • Solution: 12 goes into 144 exactly 12 times. The answer is 12.

    Advanced Example:

    • Problem: Solve 225 ÷ 15
    • Solution: 15 goes into 225 exactly 15 times. The answer is 15.

    Interactive Quiz with Feedback System​

    You do not have access to this page.

    If you are not a subscriber, please click here to subscribe.
    OR

    Common Mistakes and Pitfalls

    • Forgetting to check the remainder.
    • Confusing the order of operations.
    • Not estimating or rounding numbers before dividing.

    Tips and Tricks for Efficiency

    • Practice multiplication tables to improve division skills.
    • Use estimation to check if your answer is reasonable.
    • Break down larger numbers into smaller, easier parts.

    Real life application

    • Cooking: Adjusting recipes based on serving sizes.
    • Budgeting: Dividing expenses among friends or family.
    • Sports: Calculating scores or averages in games.

    FAQ's

    Practice regularly! Use flashcards or online games to help you memorize them.
    Yes, when the dividend does not divide evenly by the divisor, you can get a decimal or a fraction.
    A remainder is what is left over after division when the dividend cannot be divided evenly by the divisor.
    Dividing by zero is not possible because it does not make sense in mathematics; it creates an undefined situation.
    You can multiply the quotient by the divisor and see if it equals the dividend. If it does, your answer is correct.

    Conclusion

    Mastering division, especially with larger numbers, is an essential skill in mathematics. By using efficient methods and practicing regularly, you’ll become confident in your ability to divide and solve real-world problems.

    References and Further Exploration

    • Khan Academy: Interactive lessons on division.
    • Book: Math Made Easy by Thomas S. Troward.

    Like? Share it with your friends

    Facebook
    Twitter
    LinkedIn

    Filter

    • Category

    • Levels

    • Subject