MathIsimple

Three-Digit by One-Digit Division (No Remainder)

Master the art of dividing three-digit numbers by one-digit numbers! Learn powerful strategies that make long division easy and systematic.

Learning Scenario

Candy Gift Box Distribution Challenge! The school has 432 pieces of candy to distribute equally among 3 gift boxes. How many pieces of candy will go in each box? Let's solve this using the powerful step-by-step decomposition method!

What is Long Division?

Definition

Long division is a method for dividing large numbers by breaking them down into smaller, manageable steps. We work from left to right, dividing each place value and keeping track of our progress.

Think of it like this: It's like sharing a large number of items among a smaller number of people, one group at a time, until everyone gets their fair share!

Why Use Long Division?

  • •Makes large division problems manageable and organized
  • •Shows the step-by-step process clearly
  • •Helps understand place value relationships
  • •Builds foundation for more complex division problems

Step-by-Step Process: 432 ÷ 3

Step 1: Set Up the Problem

432 ÷ 3

We write this as: 3 ⟌ 432

432 is the dividend (what we're dividing)

3 is the divisor (what we're dividing by)

Step 2: Divide Hundreds Place

144
3 ⟌ 432
-3
--
13

Question: How many 3s are in 4? Answer: 1 (write 1 above the 4)

Multiply: 1 × 3 = 3 (write 3 below the 4)

Subtract: 4 - 3 = 1 (write 1 below)

Step 3: Bring Down and Divide Tens

144
3 ⟌ 432
-3
--
13
-12
---
1

Bring down: Bring down the 3 to make 13

Question: How many 3s are in 13? Answer: 4 (write 4 above the 3)

Multiply: 4 × 3 = 12 (write 12 below the 13)

Subtract: 13 - 12 = 1 (write 1 below)

Step 4: Bring Down and Divide Ones

144
3 ⟌ 432
-3
--
13
-12
---
12
-12
--
0

Bring down: Bring down the 2 to make 12

Question: How many 3s are in 12? Answer: 4 (write 4 above the 2)

Multiply: 4 × 3 = 12 (write 12 below the 12)

Subtract: 12 - 12 = 0 (no remainder!)

Final Answer

432 ÷ 3 = 144
Each gift box will contain 144 pieces of candy!

Understanding Place Value in Division

Why Each Step Matters

1

Hundreds place (4):

We can fit 1 group of 3 in 4 hundreds

4

Tens place (13):

We can fit 4 groups of 3 in 13 tens

4

Ones place (12):

We can fit 4 groups of 3 in 12 ones

The Complete Process

432 ÷ 3 = 144

1 hundred + 4 tens + 4 ones = 144

Each digit in the quotient corresponds to a place value in the dividend

Example Problems

Example 1: 648 ÷ 4

Step-by-Step Solution:

162
4 ⟌ 648
-4
--
24
-24
--
8
-8
-
0

Answer: 648 ÷ 4 = 162

Example 2: 735 ÷ 5

Step-by-Step Solution:

147
5 ⟌ 735
-5
--
23
-20
--
35
-35
--
0

Answer: 735 ÷ 5 = 147

Interactive Activities

Activity 1: Practice Long Division

Solve 528 ÷ 6 step by step:

?
6 ⟌ 528
-?
--
?

Activity 2: Real-World Problem

A school has 672 students and wants to divide them equally into 8 classes. How many students will be in each class?

⟌

Common Mistakes to Avoid

❌ Forgetting to bring down the next digit

Always bring down the next digit after each subtraction step.

❌ Not aligning numbers properly

Make sure each digit in the quotient is written above the correct place value.

❌ Rushing through the steps

Take your time with each step to avoid calculation errors.

Practice Problems

Problem 1

A factory produces 816 widgets and needs to pack them equally into 6 boxes. How many widgets will be in each box?

⟌

Problem 2

Solve: 945 ÷ 7

7 ⟌ 945

Key Takeaways

What You Learned

  • ✓Long division breaks large problems into manageable steps
  • ✓We work from left to right, one place value at a time
  • ✓Each digit in the quotient corresponds to a place value
  • ✓Practice helps build confidence and accuracy

Next Steps

  • →Practice with more three-digit division problems
  • →Learn division with remainders
  • →Apply these skills to real-world problems