Division Problems 2 Digits - Complete Guide for Grade 4 Students

Master division of 2-digit numbers by 1-digit numbers: long division method, quotients, remainders, and step-by-step solutions through comprehensive exercises and detailed explanations.

Division Problems 2 Digits - Summary
Key Definitions
Essential Terms:

Division: The process of splitting a number into equal parts or groups

Dividend: The number being divided (the larger number)

Divisor: The number that divides the dividend (the smaller number)

Quotient: The result of division (how many equal parts/groups)

Remainder: What's left over after division (if any)

2-Digit Division: Division where the dividend is a 2-digit number (10-99)

Core Rules and Laws
Fundamental Rules:

• Division Relationship: Dividend = Divisor × Quotient + Remainder

• Remainder Rule: Remainder is always less than the divisor

• Division by 1: Any number divided by 1 equals itself

• Zero Division: 0 divided by any non-zero number equals 0

• Division by Zero: Undefined (impossible)

• Inverse Operation: Division is the inverse of multiplication

Step-by-Step Method
Long Division Process:
  1. Divide: How many times does the divisor go into the current number?
  2. Multiply: Multiply the quotient digit by the divisor
  3. Subtract: Subtract the result from the current number
  4. Bring Down: Bring down the next digit
  5. Repeat: Continue until all digits are processed
  6. Check: Verify using: Divisor × Quotient + Remainder = Dividend
Examples and Tips
Simple Example: 48 ÷ 4 = 12 (no remainder)
With Remainder: 73 ÷ 5 = 14 remainder 3
Key Tip: Know multiplication tables - they're essential for division!
Check Method: Always verify: Quotient × Divisor + Remainder = Original Number
Solution: Exercises 1 to 3
1 Basic Division
Exercise 1
Find the quotient of:
\(56 \div 7\)
Understanding the Problem:

This is a basic division problem where we need to find how many times 7 goes into 56

Solution Approach:
  1. We're looking for a number that when multiplied by 7 gives us 56
  2. Think: 7 × ? = 56
  3. From multiplication tables: 7 × 8 = 56
Expression
\(56 \div 7\)
Division
\(8\)
Step 1: Set up the division

We need to divide 56 by 7

56 ÷ 7 = ?

Step 2: Use multiplication facts

Think: What number times 7 equals 56?

7 × 8 = 56

So 56 ÷ 7 = 8

Step 3: Verify the answer

Check: 8 × 7 = 56 ✓

No remainder since 56 is exactly divisible by 7

\(56 \div 7 = 8\)
Final answer:

\(56 \div 7 = 8\) with no remainder

Applied rules:

• Division as inverse of multiplication: 56 ÷ 7 = 8 because 8 × 7 = 56

• Exact division: When dividend is completely divisible by divisor

• Multiplication check: Always verify your answer

2 Division with Remainder
Exercise 2
Find the quotient and remainder of:
\(83 \div 6\)
Understanding the Problem:

This division will have a remainder since 6 doesn't divide evenly into 83

Expression
\(83 \div 6\)
Division
\(13\) R\(5\)
Step 1: Set up the division

We need to divide 83 by 6

83 ÷ 6 = ?

Step 2: Divide the tens place

How many times does 6 go into 8 (tens place)?

6 × 1 = 6, 6 × 2 = 12 (too big)

So 6 goes into 8 once (1)

Write 1 above the tens place

Step 3: Multiply and subtract

1 × 6 = 6

8 - 6 = 2

Step 4: Bring down the ones place

Bring down the 3

Now we have 23

Step 5: Divide the new number

How many times does 6 go into 23?

6 × 3 = 18, 6 × 4 = 24 (too big)

So 6 goes into 23 three times (3)

Write 3 above the ones place

Step 6: Multiply and subtract

3 × 6 = 18

23 - 18 = 5

5 is less than 6, so 5 is our remainder

\(83 \div 6 = 13\) remainder \(5\)
Final answer:

\(83 \div 6 = 13\) remainder \(5\)

Check: \(13 \times 6 + 5 = 78 + 5 = 83\) ✓

Applied rules:

• Division algorithm: Dividend = Divisor × Quotient + Remainder

• Remainder constraint: Remainder must be less than divisor

• Estimation: Use multiplication facts to determine how many times divisor fits

3 Division with Zero in Quotient
Exercise 3
Find the quotient of:
\(96 \div 8\)
Understanding the Problem:

This is an exact division where 8 divides evenly into 96

Expression
\(96 \div 8\)
Division
\(12\)
Step 1: Set up the division

We need to divide 96 by 8

96 ÷ 8 = ?

Step 2: Divide the tens place

How many times does 8 go into 9 (tens place)?

8 × 1 = 8, 8 × 2 = 16 (too big)

So 8 goes into 9 once (1)

Write 1 above the tens place

Step 3: Multiply and subtract

1 × 8 = 8

9 - 8 = 1

Step 4: Bring down the ones place

Bring down the 6

Now we have 16

Step 5: Divide the new number

How many times does 8 go into 16?

8 × 2 = 16

So 8 goes into 16 exactly two times (2)

Write 2 above the ones place

Step 6: Multiply and subtract

2 × 8 = 16

16 - 16 = 0

No remainder

\(96 \div 8 = 12\)
Final answer:

\(96 \div 8 = 12\) with no remainder

Check: \(12 \times 8 = 96\) ✓

Applied rules:

• Long division: Divide, multiply, subtract, bring down, repeat

• Multiplication check: Verify result by multiplying quotient by divisor

• Place value: Keep track of tens and ones positions

Solution: Exercises 4 to 5
4 Word Problem Application
Exercise 4
A teacher has 78 pencils to distribute equally among 6 students. How many pencils will each student receive?
Understanding the Problem:

This is a word problem requiring division to solve an equal sharing situation

Problem
\(78 \div 6\)
Division
\(13\)
Step 1: Identify the operation

Teacher has 78 pencils and 6 students

To share equally: 78 ÷ 6 = ?

Step 2: Set up the division

We need to divide 78 by 6

78 ÷ 6 = ?

Step 3: Divide the tens place

How many times does 6 go into 7 (tens place)?

6 × 1 = 6, 6 × 2 = 12 (too big)

So 6 goes into 7 once (1)

Write 1 above the tens place

Step 4: Multiply and subtract

1 × 6 = 6

7 - 6 = 1

Step 5: Bring down the ones place

Bring down the 8

Now we have 18

Step 6: Divide the new number

How many times does 6 go into 18?

6 × 3 = 18

So 6 goes into 18 exactly three times (3)

Write 3 above the ones place

Step 7: Multiply and subtract

3 × 6 = 18

18 - 18 = 0

No remainder

Step 8: Interpret the result

Each student gets 13 pencils

All pencils are distributed (no remainder)

Each student gets 13 pencils
Final answer:

Each student gets 13 pencils.

Check: \(13 \times 6 = 78\) ✓

Applied rules:

• Equal sharing: Division to distribute items equally

• Real-world context: Interpret the quotient in the problem's context

• Verification: Multiply quotient by divisor to check

5 Complex Division Problem
Exercise 5
Solve: \(91 \div 7\) and verify your answer
Understanding the Problem:

This is a division problem that may have a remainder. We need to find the quotient and verify our answer.

Expression
\(91 \div 7\)
Division
\(13\)
Step 1: Set up the division

We need to divide 91 by 7

91 ÷ 7 = ?

Step 2: Divide the tens place

How many times does 7 go into 9 (tens place)?

7 × 1 = 7, 7 × 2 = 14 (too big)

So 7 goes into 9 once (1)

Write 1 above the tens place

Step 3: Multiply and subtract

1 × 7 = 7

9 - 7 = 2

Step 4: Bring down the ones place

Bring down the 1

Now we have 21

Step 5: Divide the new number

How many times does 7 go into 21?

7 × 3 = 21

So 7 goes into 21 exactly three times (3)

Write 3 above the ones place

Step 6: Multiply and subtract

3 × 7 = 21

21 - 21 = 0

No remainder

Step 7: Verify the answer

Check: 13 × 7 = 91 ✓

Alternative check: 91 ÷ 7 = 13 ✓

\(91 \div 7 = 13\)
Final answer:

\(91 \div 7 = 13\) with no remainder

Check: \(13 \times 7 = 91\) ✓

Applied rules:

• Division verification: Always check your answer

• Multiplication facts: Knowing 7 × 13 = 91 helps solve this

• Place value: Work from tens to ones

Questions & Answers

Question: I keep getting confused about when there's a remainder and when there isn't. How can I tell if a division will have a remainder?

Answer: Great question! There are a few ways to predict if a division will have a remainder:

Method 1: Multiplication Check

  • If you can find a number that when multiplied by the divisor gives you the dividend exactly, there's no remainder
  • Example: 56 ÷ 7 → Does 7 × ? = 56? Yes, 7 × 8 = 56, so no remainder
  • Example: 58 ÷ 7 → Does 7 × ? = 58? No, 7 × 8 = 56 and 7 × 9 = 63, so there will be a remainder

Method 2: During Long Division

  • After your final subtraction, if you get 0, there's no remainder
  • If you get any number other than 0 that's less than the divisor, that's your remainder

Key Point: If the dividend is exactly divisible by the divisor (meaning the dividend is a multiple of the divisor), there will be no remainder.

Question: I sometimes get the digits mixed up in my quotient. How do I make sure I put the numbers in the right places?

Answer: This is a very common mistake! Here are strategies to keep your digits in the right places:

Strategy 1: Use Place Value Lines

  • Draw lines above your dividend to show where each digit of the quotient goes
  • For 2-digit dividends, draw two lines: _ _ (one for tens, one for ones)
  • When you divide the tens place, write the result above the tens place
  • When you divide the ones place, write the result above the ones place

Strategy 2: Think About Size

  • Look at your dividend. If it's 78, your quotient should be smaller (like 13, not 130)
  • Estimate: 78 ÷ 6 should be close to 80 ÷ 6 ≈ 13

Strategy 3: Check Your Work

  • Always verify: Quotient × Divisor + Remainder = Dividend
  • If this doesn't work, check your digit placement

Question: Why do I need to learn long division when I could just use multiplication to check my work? Isn't multiplication faster?

Answer: Long division is actually the method for finding the answer when you don't know it yet! Here's why it's important:

Long Division Purpose:

  • Long division is the process of finding the quotient when you only know the dividend and divisor
  • You use it when you need to solve problems like 83 ÷ 6, where you don't know the answer
  • Multiplication facts help during long division, but they don't replace the process

Checking Purpose:

  • Multiplication is used to verify your answer AFTER you've found it using long division
  • It's a way to catch mistakes in your calculations

Example: For 83 ÷ 6, you couldn't just "know" the answer. You need long division to find that it's 13 remainder 5. Then you check: 13 × 6 + 5 = 78 + 5 = 83 ✓

Long division builds number sense and prepares you for more complex math in higher grades!