Solved Exercises on Division Problems 2 Digit by 1 Digit in Grade 4

Master division of 2-digit numbers by 1-digit numbers: long division method, quotients, remainders, and step-by-step solutions through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic Division
Exercise 1
Find the quotient of:
\(48 \div 4\)
Definition:

Division: Finding how many times one number (divisor) goes into another number (dividend)

Quotient: The result of division (how many times the divisor fits into the dividend)

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

Long Division Method:
  1. Divide: How many times does the divisor go into the first digit(s)?
  2. Multiply: Multiply the quotient by the divisor
  3. Subtract: Subtract the result from the dividend part
  4. Bring down: Bring down the next digit
  5. Repeat: Continue until all digits are processed
Expression
\(48 \div 4\)
Division
\(12\)
Step 1: Set up the division

We need to divide 48 by 4

48 ÷ 4 = ?

Step 2: Divide the tens place

How many times does 4 go into 4 (tens place)?

4 ÷ 4 = 1

Write 1 above the tens place

Step 3: Multiply and subtract

1 × 4 = 4

4 - 4 = 0

Step 4: Bring down the ones place

Bring down the 8

Now we have 08 or just 8

Step 5: Divide the ones place

How many times does 4 go into 8?

8 ÷ 4 = 2

Write 2 above the ones place

Step 6: Multiply and subtract

2 × 4 = 8

8 - 8 = 0

No remainder

\(48 \div 4 = 12\)
Final answer:

\(48 \div 4 = 12\) with no remainder

Applied rules:

• Division: How many groups of the divisor fit in the dividend?

• Multiplication check: 12 × 4 = 48 ✓

• Place value: Work from left to right (tens then ones)

2 Division with Remainder
Exercise 2
Find the quotient and remainder of:
\(73 \div 5\)
Definition:

Division with remainder: When the divisor doesn't divide evenly into the dividend

Remainder: The amount left over after division (always less than the divisor)

Expression
\(73 \div 5\)
Division
\(14\) R\(3\)
Step 1: Set up the division

We need to divide 73 by 5

73 ÷ 5 = ?

Step 2: Divide the tens place

How many times does 5 go into 7 (tens place)?

5 × 1 = 5, 5 × 2 = 10 (too big)

So 5 goes into 7 once (1)

Write 1 above the tens place

Step 3: Multiply and subtract

1 × 5 = 5

7 - 5 = 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 5 go into 23?

5 × 4 = 20, 5 × 5 = 25 (too big)

So 5 goes into 23 four times (4)

Write 4 above the ones place

Step 6: Multiply and subtract

4 × 5 = 20

23 - 20 = 3

3 is less than 5, so 3 is our remainder

\(73 \div 5 = 14\) remainder \(3\)
Final answer:

\(73 \div 5 = 14\) remainder \(3\)

Check: \(14 \times 5 + 3 = 70 + 3 = 73\) ✓

Applied rules:

• Remainder rule: Remainder must be less than the divisor

• Division check: Quotient × Divisor + Remainder = Original Number

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

3 Division with Zero in Quotient
Exercise 3
Find the quotient of:
\(84 \div 7\)
Definition:

Division with zero in quotient: When the divisor doesn't go into the partial dividend

Partial dividend: The number formed by bringing down digits

Expression
\(84 \div 7\)
Division
\(12\)
Step 1: Set up the division

We need to divide 84 by 7

84 ÷ 7 = ?

Step 2: Divide the tens place

How many times does 7 go into 8 (tens place)?

7 × 1 = 7, 7 × 2 = 14 (too big)

So 7 goes into 8 once (1)

Write 1 above the tens place

Step 3: Multiply and subtract

1 × 7 = 7

8 - 7 = 1

Step 4: Bring down the ones place

Bring down the 4

Now we have 14

Step 5: Divide the new number

How many times does 7 go into 14?

7 × 2 = 14

So 7 goes into 14 exactly two times (2)

Write 2 above the ones place

Step 6: Multiply and subtract

2 × 7 = 14

14 - 14 = 0

No remainder

\(84 \div 7 = 12\)
Final answer:

\(84 \div 7 = 12\) with no remainder

Check: \(12 \times 7 = 84\) ✓

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

Division Rules and Methods
\(\text{Dividend} \div \text{Divisor} = \text{Quotient}\)
Basic Division Formula
Division Relationship
\(\text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder}\)
Always holds true
Remainder Rule
\(\text{Remainder} < \text{Divisor}\)
Remainder is always smaller
Division Check
\(\text{Quotient} \times \text{Divisor} + \text{Remainder} = \text{Original Number}\)
Verification method
Key Definitions:

Dividend: The number being divided (the larger number)

Divisor: The number dividing the dividend (the smaller number)

Quotient: The result of division (how many times divisor fits)

Remainder: What's left over after division

Long Division Steps:
  1. Divide: How many times does divisor go into current number?
  2. Multiply: Multiply quotient digit by divisor
  3. Subtract: Subtract result from current number
  4. Bring Down: Bring down next digit
  5. Repeat: Continue until all digits processed
Tip 1: Know your multiplication tables! They're essential for division.
Tip 2: Always check your answer: Quotient × Divisor + Remainder = Original Number.
Tip 3: The remainder is always less than the divisor.
Tip 4: Start with the highest place value (tens, then ones).
Common errors: Forgetting to bring down the next digit, miscalculating multiplication facts, placing digits in wrong positions.
Exam preparation: Practice with various divisors (2, 3, 4, 5, 6, 7, 8, 9), focus on place value, always check answers.
Division Facts to Remember:

• Division is the inverse of multiplication

• Any number divided by 1 equals itself

• Zero divided by any number (except 0) equals 0

• Division by zero is undefined

• Remainder must always be less than the divisor

Solution: Exercises 4 to 5
4 Division with Remainder
Exercise 4
Find the quotient and remainder of:
\(95 \div 6\)
Definition:

Division with remainder: When the divisor doesn't divide evenly into the dividend

Partial quotient: The number of times the divisor goes into part of the dividend

Expression
\(95 \div 6\)
Division
\(15\) R\(5\)
Step 1: Set up the division

We need to divide 95 by 6

95 ÷ 6 = ?

Step 2: Divide the tens place

How many times does 6 go into 9 (tens place)?

6 × 1 = 6, 6 × 2 = 12 (too big)

So 6 goes into 9 once (1)

Write 1 above the tens place

Step 3: Multiply and subtract

1 × 6 = 6

9 - 6 = 3

Step 4: Bring down the ones place

Bring down the 5

Now we have 35

Step 5: Divide the new number

How many times does 6 go into 35?

6 × 5 = 30, 6 × 6 = 36 (too big)

So 6 goes into 35 five times (5)

Write 5 above the ones place

Step 6: Multiply and subtract

5 × 6 = 30

35 - 30 = 5

5 is less than 6, so 5 is our remainder

\(95 \div 6 = 15\) remainder \(5\)
Final answer:

\(95 \div 6 = 15\) remainder \(5\)

Check: \(15 \times 6 + 5 = 90 + 5 = 95\) ✓

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

5 Word Problem Application
Exercise 5
Sarah has 63 stickers. She wants to share them equally among 7 friends. How many stickers will each friend get?
Definition:

Word problems: Real-life situations requiring mathematical operations

Equal sharing: Division to distribute items equally

Problem
\(63 \div 7\)
Division
\(9\)
Step 1: Identify the operation

Sarah has 63 stickers and 7 friends

To share equally: 63 ÷ 7 = ?

Step 2: Set up the division

We need to divide 63 by 7

63 ÷ 7 = ?

Step 3: Divide the tens place

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

Since 7 > 6, consider 63 (both digits together)

7 × 9 = 63

So 7 goes into 63 nine times (9)

Step 4: Multiply and subtract

9 × 7 = 63

63 - 63 = 0

No remainder

Step 5: Interpret the result

Each friend gets 9 stickers

All stickers are distributed (no remainder)

Each friend gets 9 stickers
Final answer:

Each friend gets 9 stickers.

Check: \(9 \times 7 = 63\) ✓

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

Division Laws, Methods, Rules, and Key Concepts
\(\text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder}\)
Division Algorithm
Key definitions:

Division: The process of splitting a number into equal parts

Dividend: The number being divided (the total amount)

Divisor: The number by which the dividend is divided (the number of groups)

Quotient: The result of division (size of each group)

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

Complete Division Methodology:
  1. Read the problem: Identify dividend and divisor
  2. Set up the division: Write in long division format
  3. Divide: Determine how many times divisor goes into current number
  4. Multiply: Multiply quotient digit by divisor
  5. Subtract: Subtract result from current number
  6. Bring down: Bring down the next digit
  7. Repeat: Continue until all digits are processed
  8. Check: Verify using multiplication
Tip 1: Know your multiplication facts! Division relies heavily on knowing multiplication.
Tip 2: The remainder is always less than the divisor. If it's not, you made a mistake!
Tip 3: Always check your answer: Quotient × Divisor + Remainder = Original Number.
Tip 4: Work from left to right, starting with the highest place value.
Common errors: Forgetting to bring down the next digit, miscalculating multiplication facts, placing digits in wrong positions, ignoring remainders.
Exam preparation: Practice with various divisors (2-9), focus on place value, always check answers, work on word problems.
Division Rules to Remember:

• Division is the inverse operation of multiplication

• Any number divided by 1 equals the original number

• Zero divided by any non-zero number equals zero

• Division by zero is undefined (not possible)

• The remainder must always be less than the divisor

• Dividend = Divisor × Quotient + Remainder (always true)

Questions & Answers

Question: I don't understand why we need to know multiplication facts to do division. Can you explain how they're connected?

Answer: Great question! Division and multiplication are inverse operations - they undo each other. When solving 48 ÷ 6, you're asking "What number multiplied by 6 gives me 48?"

For example:

  • If you know 6 × 8 = 48, then you know 48 ÷ 6 = 8
  • If you know 7 × 9 = 63, then you know 63 ÷ 7 = 9
  • If you know 4 × 12 = 48, then you know 48 ÷ 4 = 12

In long division, when you divide 73 by 5, you need to figure out "How many 5s are in 7?" The answer comes from knowing that 5 × 1 = 5 and 5 × 2 = 10 (which is too big). So you use 1. This is why strong multiplication skills make division much easier!

Question: I sometimes forget whether to write 0 in the quotient when the divisor doesn't go into the partial dividend. How do I know when to put 0?

Answer: You only write 0 in the quotient when the divisor is larger than the current partial dividend AND there are more digits to bring down.

For example, in 804 ÷ 4:

  • 4 goes into 8 two times (write 2)
  • 4 goes into 0 zero times (write 0)
  • 4 goes into 4 one time (write 1)

But in 84 ÷ 7:

  • 7 goes into 8 one time (write 1)
  • After subtraction, we have 1, then bring down 4 to make 14
  • 7 goes into 14 two times (write 2)

The key is: if the divisor is bigger than the current number but you have more digits to bring down, you still write 0. If you've processed all digits, then you're done.

Question: I always struggle with checking my division answers. What's the easiest way to verify if my quotient is correct?

Answer: The most reliable way to check division is using the relationship: Dividend = Divisor × Quotient + Remainder

For example, if you calculated 73 ÷ 5 = 14 remainder 3:

Check: 5 × 14 + 3 = 70 + 3 = 73 ✓

Another example: If you calculated 48 ÷ 4 = 12:

Check: 4 × 12 + 0 = 48 + 0 = 48 ✓

This method works every time and helps catch calculation errors. It's especially important for problems with remainders - don't forget to add the remainder back!

Practice this checking method regularly - it will help build confidence in your division skills.