Solved Exercises on Multi-Digit Operations in Grade 4

Master multi-digit operations: addition, subtraction, multiplication, and division of multi-digit numbers through these 5 detailed exercises.

Multi-Digit Operations: Complete Guide
Core Concepts & Definitions

Multi-Digit Operations: Mathematical operations (addition, subtraction, multiplication, division) performed with numbers that have more than one digit.

Place Value: The value of a digit based on its position in the number (ones, tens, hundreds, thousands, etc.).

Regrouping: Carrying over or borrowing from higher place values during operations.

Partial Products: Breaking down multiplication into smaller parts based on place value.

➕
Addition
➖
Subtraction
✖️
Multiplication
➗
Division
Addition Algorithm

Line up numbers by place value

Add digits column by column

Carry over when sum ≥ 10

Subtraction Algorithm

Line up numbers by place value

Subtract digits column by column

Borrow when needed

Multiplication Algorithm

Multiply each digit of the bottom number

Shift partial products

Add all partial products

Addition
Combining numbers to find their total sum. Regroup when a column adds up to 10 or more.
Subtraction
Finding the difference between numbers. Borrow from higher place values when needed.
Multiplication
Repeated addition of a number. Use place value to multiply correctly.
Division
Splitting a number into equal groups. May result in a remainder.
Step-by-Step Operation Process
  1. Align numbers: Line up numbers by place value (rightmost digits aligned)
  2. Start from right: Begin calculations in the ones place
  3. Move left: Work through each place value column
  4. Regroup when needed: Carry over for addition, borrow for subtraction
  5. Check your work: Verify using inverse operations or estimation
Key Place Values

Ones (1)

Tens (10)

Hundreds (100)

Thousands (1,000)

Ten Thousands (10,000)

Verification Methods

Addition: Subtract one addend from sum

Subtraction: Add subtrahend to difference

Multiplication: Divide product by one factor

Division: Multiply quotient by divisor

Tips for Multi-Digit Operations Success
  • Always align numbers properly by place value
  • Work slowly and carefully to avoid mistakes
  • Check your work by using inverse operations
  • Estimate first to see if your answer makes sense
  • Practice regrouping/borrowing regularly
  • Use scratch paper to organize your work
  • Pay attention to place value when multiplying
Multi-Digit Operations Exercises: 1 to 3
1 Multi-digit addition
Exercise 1
Add: 4,287 + 3,569
Definition:

Multi-digit addition: Adding numbers with multiple digits, working from right to left and carrying over when necessary

Addition method:
  1. Align numbers by place value
  2. Add digits in each column from right to left
  3. Carry over when sum is 10 or greater
  4. Continue until all columns are added
Problem
4,287 + 3,569
Solution
7,856
Step 1: Align numbers by place value

4,287

+ 3,569

------

Step 2: Add ones column (7 + 9)

7 + 9 = 16 → Write 6, carry 1

Step 3: Add tens column (8 + 6 + 1)

8 + 6 + 1 = 15 → Write 5, carry 1

Step 4: Add hundreds column (2 + 5 + 1)

2 + 5 + 1 = 8

Step 5: Add thousands column (4 + 3)

4 + 3 = 7

4,287 + 3,569 = 7,856
Final answer:

4,287 + 3,569 = 7,856

Applied rules:

• Place value alignment: Numbers lined up by place value

• Carrying: When sum ≥ 10, carry the tens digit to next column

• Verification: 7,856 - 3,569 = 4,287 ✓

🔢
First Number
4,287
➕
Operation
+
🔢
Second Number
3,569
🟰
Sum
7,856
2 Multi-digit subtraction
Exercise 2
Subtract: 8,432 - 5,768
Definition:

Multi-digit subtraction: Subtracting numbers with multiple digits, working from right to left and borrowing when necessary

Problem
8,432 - 5,768
Solution
2,664
Step 1: Align numbers by place value

8,432

- 5,768

------

Step 2: Subtract ones column (2 - 8)

Need to borrow: 12 - 8 = 4

Step 3: Subtract tens column (2 - 6)

After borrowing: 12 - 6 = 6

Step 4: Subtract hundreds column (3 - 7)

After borrowing: 13 - 7 = 6

Step 5: Subtract thousands column (7 - 5)

7 - 5 = 2

8,432 - 5,768 = 2,664
Final answer:

8,432 - 5,768 = 2,664

Applied rules:

• Place value alignment: Numbers lined up by place value

• Borrowing: When top digit is smaller, borrow from next column

• Verification: 2,664 + 5,768 = 8,432 ✓

🔢
Minuend
8,432
➖
Operation
-
🔢
Subtrahend
5,768
🟰
Difference
2,664
3 Multi-digit multiplication
Exercise 3
Multiply: 347 × 26
Definition:

Multi-digit multiplication: Multiplying numbers with multiple digits using partial products and place value

Problem
347 × 26
Solution
9,022
Step 1: Multiply 347 by 6 (ones place)

347 × 6 = 2,082

Step 2: Multiply 347 by 20 (tens place)

347 × 20 = 6,940

Step 3: Add the partial products

2,082 + 6,940 = 9,022

347 × 26 = 9,022
Final answer:

347 × 26 = 9,022

Applied rules:

• Partial products: Multiply each digit separately

• Place value: Shift second row one place to the left

• Verification: 9,022 ÷ 26 = 347 ✓

🔢
Factor 1
347
✖️
Operation
×
🔢
Factor 2
26
🟰
Product
9,022
Operation Rules & Methods
a + b = c
Addition
Addition
a + b = c
Combining numbers
Subtraction
a - b = c
Finding difference
Multiplication
a × b = c
Repeated addition
Division
a ÷ b = c R r
Splitting into groups
Key definitions:

Addition: Combining two or more numbers to find their total

Subtraction: Finding the difference between two numbers

Multiplication: Repeated addition of the same number

Division: Splitting a number into equal groups

Complete methodology:
  1. Identify operation: Determine which operation to perform
  2. Align numbers: Line up by place value
  3. Follow algorithm: Use the appropriate method for the operation
  4. Check work: Verify using inverse operation
Tip 1: Always align numbers properly by place value.
Tip 2: Work slowly and carefully to avoid mistakes.
Tip 3: Check your work by using inverse operations.
Tip 4: Estimate first to see if your answer makes sense.
Common errors: Misaligning numbers, forgetting to carry/borrow, place value mistakes.
Key notes: Place value is crucial for all multi-digit operations.
Important rules to remember:

• Alignment: Always line up numbers by place value

• Carrying: In addition, carry when sum ≥ 10

• Borrowing: In subtraction, borrow when top digit is smaller

• Partial products: In multiplication, multiply each digit separately

➕
Addition
Combine numbers, carry when needed
➖
Subtraction
Find difference, borrow when needed
✖️
Multiplication
Repeated addition, partial products
Multi-Digit Operations Exercises: 4 to 5
4 Multi-digit division
Exercise 4
Divide: 8,924 ÷ 12
Definition:

Multi-digit division: Dividing larger numbers using the standard algorithm, finding how many times the divisor fits into the dividend

Problem
8,924 ÷ 12
Solution
743 R 8
Step 1: Set up the division

Divide 8,924 by 12

Step 2: Divide 89 by 12

12 goes into 89 seven times (7 × 12 = 84)

Step 3: Bring down next digit (2)

89 - 84 = 5, bring down 2 → 52

Step 4: Divide 52 by 12

12 goes into 52 four times (4 × 12 = 48)

Step 5: Bring down last digit (4)

52 - 48 = 4, bring down 4 → 44

Step 6: Divide 44 by 12

12 goes into 44 three times (3 × 12 = 36), remainder 8

8,924 ÷ 12 = 743 R 8
Final answer:

8,924 ÷ 12 = 743 R 8

Applied rules:

• Division algorithm: Divide, multiply, subtract, bring down

• Remainder: What's left after last subtraction

• Verification: 743 × 12 + 8 = 8,916 + 8 = 8,924 ✓

🔢
Dividend
8,924
➗
Operation
÷
🔢
Divisor
12
🟰
Quotient R Rem
743 R 8
5 Mixed operations
Exercise 5
Solve: (2,437 + 1,896) - 1,542
Definition:

Mixed operations: Problems that combine different mathematical operations, following order of operations

Problem
(2,437 + 1,896) - 1,542
Solution
2,791
Step 1: Solve inside parentheses first

2,437 + 1,896 = 4,333

Step 2: Perform subtraction

4,333 - 1,542 = 2,791

Step 3: Verify the addition

2,437 + 1,896: 7 + 6 = 13 → carry 1, continue...

Step 4: Verify the subtraction

4,333 - 1,542: Need to borrow in tens place...

(2,437 + 1,896) - 1,542 = 2,791
Final answer:

(2,437 + 1,896) - 1,542 = 2,791

Applied rules:

• Order of operations: Parentheses first

• Addition algorithm: Add from right to left with carrying

• Subtraction algorithm: Subtract from right to left with borrowing

➕
First Step
4,333
➖
Second Step
2,791
🟰
Final Result
2,791

Questions & Answers

Question: I keep making mistakes when adding multi-digit numbers. What's the best way to avoid errors?

Answer: Here are some effective strategies to avoid errors in multi-digit addition:

  • Always line up numbers by place value (ones under ones, tens under tens, etc.)
  • Work slowly and carefully, especially when carrying
  • Check each column as you go to catch mistakes early
  • Estimate first to see if your answer makes sense
  • Go back and verify your answer by subtracting one number from the sum

For example, if adding 3,456 + 2,789, estimate: 3,500 + 2,800 = 6,300. Your answer should be close to this.

Question: My child struggles with borrowing in subtraction. How can I help them understand this concept better?

Answer: Borrowing can be challenging! Here are ways to help:

  • Use base-10 blocks or visual aids to show the concept concretely
  • Explain that borrowing means taking from the next higher place value
  • Practice with simpler problems first (like 2-digit numbers)
  • Emphasize that borrowing changes the original number: 1 ten becomes 10 ones
  • Have them say the borrowing aloud: "I need to borrow 1 from the tens place"

For example, in 52 - 18, you can't subtract 8 from 2, so you borrow 1 ten (making 12 ones) from the 5 tens (leaving 4 tens).

Question: How do I know if my multi-digit multiplication answer is correct?

Answer: There are several ways to check your multiplication:

  • Estimate first: Round numbers and multiply to see if your answer is reasonable
  • Reverse operation: Divide your product by one of the factors to see if you get the other factor
  • Use a calculator to verify
  • Redo the problem using a different method (like the lattice method)

For example, if 24 × 17 = 408, check: 408 ÷ 17 = 24 or 408 ÷ 24 = 17. Also, estimate: 25 × 20 = 500, so 408 is reasonable.