Use Sharing to Divide Two Digit Divisors

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.