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
- 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. - Divide 460 ÷ 50, use long division to find the quotient.
- Draw an area model to find the quotient of 195 ÷ 13.
- Estimate 451 ÷ 20.
- Estimate to find the quotient of 4,618 ÷ 32.
- Draw an area model to find the quotient of 3,710 ÷ 16.
- Use the long division to find the quotient of 233 ÷ 11.
- Draw an area model to find the quotient of 780 ÷ 60.
- Estimate and draw an area model to find the quotient of 715 ÷ 23.
- 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
Related topics
Square 1 to 20 : Chart, Table, Perfect Squares and Examples
Square 1 to 20 When you multiply a number by itself, the result is called a square. And when you’re preparing for exams, you need to have a foundation for algebra and quick mental math because you get a really short time to do your exam. Therefore, learning the squares from one to twenty is […]
Square 1 to 40 : Table, Perfect Squares, Chart and Examples
Square 1 to 40 When you multiply a number by itself, the resulting number is a square, and if you are someone who is either appearing in a competitive exam or just wants to do well in math in school, knowing square 1 to 40 is a really important skill. But manually multiplying every time, […]
Square Root : Definition, Formula, Methods and Types Explained
Square Root Square roots are one of those seemingly daunting maths topics that appear in many different situations, from algebra to geometry. Yet the concepts behind them aren’t as hard to grasp. It makes handling numbers far easier if you know the concept well. Let us understand how to find the square roots of a number […]
Cubes 1 to 20 : Chart, Table, Memory Tricks and Examples
Most students don’t struggle much with smaller cubes like 2³ or 3³. Those usually come quickly. The hesitation starts with numbers like 11³ or 17³. Or when someone suddenly asks, what is 20 cubed? That pause is not a memory problem. It’s about the lack of proper understanding and hence confidence. Naturally, learning cubes 1 […]
Other topics
Comments: