Use Models to Divide Whole Numbers

Key Concepts

• Division with estimation
• Division with an area model

Introduction

• Find the quotients of greater dividends.
• Draw an area model to find the quotient.
• Find the estimation to division problems.
• Estimate the division problems and check the reasonableness.
• Use area models to find the quotients.
• Solve division problems using division strategies.

Division with estimation

Example 1:

A publishing house has four printers in 4 rooms. The printer in room 3 is used by all the 15 employees of the house. The pages available in the room are distributed equally among the employees. Find the total pages used by each employee.

Solution:

First, we have to find the estimation for the given problem.

Estimation: 3,330 ÷ 15, which is close to 3000 ÷ 15 = 200.

3,000 + 300 + 30 = 3,330

3,330 ÷ 15 = 200 + 20 + 2 = 222.

Each employee can print 222 pages.

Check for reasonableness:

15 × 200 + 15 × 20 + 15 × 2 = 3000 + 300 + 30 = 3,330.

Example 2:

Estimate and then find the quotient of 510 ÷ 30.

Solution:

Estimation: 510 ÷ 30 is close to 500 ÷ 25 = 20.

Use the long division method to find the quotient.

The quotient is 17.   

Division with an area model

Example 3:

A fruit vendor picked 1,380 grapefruits. He plans to sell the grapefruits by packing them into gift bags with 10 grapefruits in each gift bag. Find the number of gift bags that the vendor makes.

Solution:

Area Model:

1000 + 300 + 80 = 1,380

1,380 ÷ 10 = 100 + 30 + 8 = 138.

 The fruit vendor makes 138 gift bags.

Example 4:

Divide 3,657 ÷ 23.

Solution:

Area model:

∴ The quotient is 159.  

Exercise

1. The cricket coach spends an amount of $780 along with a tax of $60 to buy 20 shirts for the team. The
   cost of each shirt is $780. Find the price for one shirt before the tax was added.
2. Divide 460 ÷ 50, use long division to find the quotient.
3. Draw an area model to find the quotient of 195 ÷ 13.
4. Estimate 451 ÷ 20.
5. Estimate to find the quotient of 4,618 ÷ 32.
6. Draw an area model to find the quotient of 3,710 ÷ 16.
7. Use the long division to find the quotient of 233 ÷ 11.
8. Draw an area model to find the quotient of 780 ÷ 60.
9. Estimate and draw an area model to find the quotient of 715 ÷ 23.
10. Find the quotient of 304 ÷ 15.

Concept Map

What We Have Learned

• Find the quotients of greater dividends.
• Draw an area model to find the quotient.
• Find the estimation to division problems.
• Estimate the division problems and check the reasonableness.
• Use area models to find the quotients.
• Solve division problems using division strategies