## Key Concepts

- Applying properties to division
- Estimation and dividing the numbers
- Division of greater numbers

### Introduction

#### Division algorithm using base 10 blocks

Let us consider an example of a class that has 484 cardboard boxes for an art project. Each student needs 11 boxes. Find the number of groups of 11 boxes that can be made out of 484 objects.

We can write this as 484 ÷ 11

To solve the above division problem, we use base 10 blocks as an area model.

**Step 1:**

First, find the number of groups of 11 using base 10 blocks. Draw an image of base 10 blocks.

Now, we have to find the number of groups of 11.

**Step 2:**

Use the long division method to solve the problem.

∴

44 groups of 11 cardboard boxes can be formed out of 484 objects.

**Example 1:**

A truck worker has 258 trays to load in 12 rows. How many trays will be in each row?

**Solution:**

**Area model method:**

Use base 10 blocks to divide 258 ÷ 12

Estimate the division using place values,

258 ÷ 12 rounds to its nearest place values

258 – 250

12 – 10

258 ÷ 12 is close to 250 ÷ 10 = 25.

Regrouping the blocks to load the 12 rows.

12 × 20 = 240 12 × 1 = 12

258 – 240 = 18 18 – 12 = 6

240 + 12 = 252

So, 258 ÷ 12 = 21 + remainder 6

**Long division method:**

∴ There are 21 trays in each row with 6 trays leftover.

### Use sharing to divide: greater dividends

**How can you divide with a two–digit divisor and a four–digit dividend?**

**Example 1:**

John works at a grocery shop. The shop received delivery of 1240 chocolates. The chocolates are distributed among 10 boxes. How many chocolates should John pack in each box?

**Solution:**

**Area model method:**

Regrouping thousands into hundreds.

10 × 100 = 1000 10 × 20 = 200 10 × 4 = 40

1,240 – 1000 = 240 240 – 200 = 40 40 – 40 = 0

1000 + 200 + 40 = 1,240

So, 1,240 ÷ 12 = 124

**Long division method:**

1,240 ÷ 10 = 124

∴ There are 124 chocolates in each packing box with no chocolate leftover.

**Example 2:**

Divide 4,108 ÷ 82.

**Solution: **

Divide the given problem using the long division method.

∴ 4,108 ÷ 82 = 50 + remainder 8.

## Exercise

- Divide 299 + 13. Draw an area model for the division.
- Divide 308 + 14. Use long division to solve the problem.
- Use place value blocks to divide 5,500 + 90.
- Draw an area model to divide 3,418 + 16.
- Estimate the quotient of 4,839 + 15 to the nearest hundred.
- Divide 250 + 50.
- Divide 492 +79.
- Divide 867 + 68. Draw an area model for the division.
- Use place value blocks to divide 966 + 23.
- Draw an area model to divide 916 + 40.

### What have we learnt

- Division of numbers with area models.
- Estimation of divisors using place values.
- Estimation of dividends using place values.
- Solve division problems using place value blocks.
- Draw an area model to divide.
- Understand how to use long division method to divide.

### Summary

**Dividend:** The number that is divided in the division process.

**Divisor:** The number by which a dividend is divided is known asa divisor.

Quotient: The quotients a result that we get in the division process.

Remainder: The remainder is the amount that is left over after performing the division.

**Area Model:** An area model is a rectangular diagram or model used to solve multiplication and

division problems.

**Long division:** The process to solve a division problem.

**Place value blocks:** Place value blocks are mathematics manipulatives that are used to perform

operations of numbers.

#### Related topics

#### Addition and Multiplication Using Counters & Bar-Diagrams

Introduction: We can find the solution to the word problem by solving it. Here, in this topic, we can use 3 methods to find the solution. 1. Add using counters 2. Use factors to get the product 3. Write equations to find the unknown. Addition Equation: 8+8+8 =? Multiplication equation: 3×8=? Example 1: Andrew has […]

Read More >>#### Dilation: Definitions, Characteristics, and Similarities

Understanding Dilation A dilation is a transformation that produces an image that is of the same shape and different sizes. Dilation that creates a larger image is called enlargement. Describing Dilation Dilation of Scale Factor 2 The following figure undergoes a dilation with a scale factor of 2 giving an image A’ (2, 4), B’ […]

Read More >>#### How to Write and Interpret Numerical Expressions?

Write numerical expressions What is the Meaning of Numerical Expression? A numerical expression is a combination of numbers and integers using basic operations such as addition, subtraction, multiplication, or division. The word PEMDAS stands for: P → Parentheses E → Exponents M → Multiplication D → Division A → Addition S → Subtraction Some examples […]

Read More >>#### System of Linear Inequalities and Equations

Introduction: Systems of Linear Inequalities: A system of linear inequalities is a set of two or more linear inequalities in the same variables. The following example illustrates this, y < x + 2…………..Inequality 1 y ≥ 2x − 1…………Inequality 2 Solution of a System of Linear Inequalities: A solution of a system of linear inequalities […]

Read More >>
Comments: