Table of Contents

Division of 2-digit numbers Level 4

Introduction

Have you ever shared a pizza with friends and wondered how many slices each person gets? Division helps us solve problems like this! In this article, we will explore the division of 2-digit numbers, learning strategies and understanding remainders along the way. Let’s dive into the world of division!

Definition and Concept

Division is the process of splitting a number into equal parts. When we divide, we are finding out how many times one number fits into another. For example, in the problem 84 ÷ 12, we want to find out how many times 12 fits into 84.

Key Terms:

  • Dividend: The number being divided (e.g., 84).
  • Divisor: The number you are dividing by (e.g., 12).
  • Quotient: The result of the division (e.g., 7).
  • Remainder: What is left over after division (if applicable).

Historical Context or Origin​

The concept of division dates back thousands of years. Ancient civilizations like the Egyptians and Babylonians used division to manage resources and trade. The symbols and methods we use today evolved over time, making division easier and more systematic.

Understanding the Problem

When we divide 2-digit numbers, we often break the process into manageable steps. Let’s look at a sample problem to understand this better:

Example Problem: 72 ÷ 8

  • Identify the dividend (72) and the divisor (8).
  • Determine how many times 8 fits into 72.

Methods to Solve the Problem with different types of problems​

Method 1: Long Division
Long division is a step-by-step process for dividing larger numbers.

Example: 72 ÷ 8

  1. Set up the long division: 8 into 72.
  2. Ask, “How many times does 8 fit into 72?” The answer is 9, since 8 x 9 = 72.
  3. Write 9 above the dividend, and since there’s no remainder, we’re done!

Method 2: Repeated Subtraction
This method involves subtracting the divisor from the dividend until you reach zero or a number smaller than the divisor.

Example: 72 ÷ 8

  1. Start with 72. Subtract 8 repeatedly: 72 – 8 = 64.
  2. Repeat: 64 – 8 = 56, 56 – 8 = 48, 48 – 8 = 40, 40 – 8 = 32, 32 – 8 = 24, 24 – 8 = 16, 16 – 8 = 8, 8 – 8 = 0.
  3. Count the number of times you subtracted: 9 times!

Exceptions and Special Cases​

Remainders: Sometimes, the division does not come out evenly. For example, 85 ÷ 6. Here, 6 fits into 85 a total of 14 times (since 6 x 14 = 84), leaving a remainder of 1. So we can say:

85 ÷ 6 = 14 R1

Step-by-Step Practice​

Problem 1: Solve 96 ÷ 12.

Solution:

  1. Set up the long division: 12 into 96.
  2. 12 fits into 96 a total of 8 times.
  3. Write 8 above the dividend. There’s no remainder.

Problem 2: Solve 74 ÷ 5.

Solution:

  1. Set up the long division: 5 into 74.
  2. 5 fits into 74 a total of 14 times (5 x 14 = 70).
  3. Subtract: 74 – 70 = 4 (this is the remainder).

Examples and Variations

Example 1: 54 ÷ 9
9 fits into 54 a total of 6 times. Answer: 6.

Example 2: 63 ÷ 4
4 fits into 63 a total of 15 times with a remainder of 3. Answer: 15 R3.

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 include the remainder in the answer.
  • Misplacing decimal points when working with larger numbers.
  • Confusing the dividend and divisor.

Tips and Tricks for Efficiency

  • Practice multiplication tables to make division easier.
  • Estimate the answer before calculating to check your work.
  • Use rounding to simplify division when necessary.

Real life application

  • Sharing food among friends or family.
  • Dividing a budget for spending.
  • Calculating distances when traveling.

FAQ's

A remainder is what is left over after division when the numbers do not divide evenly.
No, division by zero is undefined in mathematics.
You can multiply the quotient by the divisor and add the remainder to see if it equals the dividend.
Practice is key! Review the steps, and with time, it will become easier.
Yes! Knowing multiplication tables and using estimation can help speed up the process.

Conclusion

Understanding how to divide 2-digit numbers is an essential math skill that helps us solve everyday problems. By practicing different methods and applying division in real-life situations, you’ll become more confident in your math abilities.

References and Further Exploration

  • Khan Academy: Interactive lessons on division.
  • Book: Math Made Easy by Thomas J. McGowan.

Like? Share it with your friends

Facebook
Twitter
LinkedIn

Filter

  • Category

  • Levels

  • Subject