Solved Exercises on Adding Multi-Digit Numbers in Grade 3

Master adding multi-digit numbers: place value, carrying, and regrouping strategies through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Adding two-digit numbers
Exercise 1
Add:
\(24 + 38\)
Definition:

Place value: Each digit has a value based on its position (ones, tens, hundreds...)

Addition method:
  1. Align numbers by place value (ones under ones, tens under tens)
  2. Add digits in each column starting from the right
  3. If sum is 10 or more, carry the extra to the next column
Numbers
\(\begin{array}{c@{}c@{}c} & 2 & 4 \\ + & 3 & 8 \\ \hline \end{array}\)
Carry
\(\begin{array}{c@{}c@{}c} ^{1} & & \\ & 2 & 4 \\ + & 3 & 8 \\ \hline & & \\ \end{array}\)
Result
\(\begin{array}{c@{}c@{}c} ^{1} & & \\ & 2 & 4 \\ + & 3 & 8 \\ \hline & 6 & 2 \\ \end{array}\)
Step 1: Align by place value

\(24 + 38\) → Write 24 above 38, aligning ones and tens columns

Step 2: Add the ones column

\(4 + 8 = 12\), write down 2 and carry 1 to the tens column

Step 3: Add the tens column with carry

\(2 + 3 + 1 = 6\), write down 6

\(24 + 38 = 62\)
Final answer:

\(24 + 38 = 62\)

Applied rules:

• Place value alignment: Always align digits by their place value

• Carrying: When sum is 10 or more, carry the extra to the next column

• Column addition: Add one column at a time from right to left

2 Adding three-digit numbers
Exercise 2
Add:
\(156 + 274\)
Definition:

Regrouping: Process of making groups of tens when adding numbers

Numbers
\(\begin{array}{c@{}c@{}c@{}c} & 1 & 5 & 6 \\ + & 2 & 7 & 4 \\ \hline \end{array}\)
Carry
\(\begin{array}{c@{}c@{}c@{}c} ^{1} & ^{1} & & \\ & 1 & 5 & 6 \\ + & 2 & 7 & 4 \\ \hline & & & \\ \end{array}\)
Result
\(\begin{array}{c@{}c@{}c@{}c} ^{1} & ^{1} & & \\ & 1 & 5 & 6 \\ + & 2 & 7 & 4 \\ \hline & 4 & 3 & 0 \\ \end{array}\)
Step 1: Align by place value

\(156 + 274\) → Write 156 above 274, aligning hundreds, tens, and ones columns

Step 2: Add the ones column

\(6 + 4 = 10\), write down 0 and carry 1 to the tens column

Step 3: Add the tens column with carry

\(5 + 7 + 1 = 13\), write down 3 and carry 1 to the hundreds column

Step 4: Add the hundreds column with carry

\(1 + 2 + 1 = 4\), write down 4

\(156 + 274 = 430\)
Final answer:

\(156 + 274 = 430\)

Applied rules:

• Three-digit addition: Same process as two-digit but includes hundreds column

• Multiple carries: May need to carry in multiple columns

• Regrouping: Process of making groups of tens when adding numbers

3 Adding four-digit numbers
Exercise 3
Add:
\(2,345 + 1,876\)
Definition:

Expanded form: Writing numbers to show the value of each digit

Numbers
\(\begin{array}{c@{}c@{}c@{}c@{}c} & 2 & 3 & 4 & 5 \\ + & 1 & 8 & 7 & 6 \\ \hline \end{array}\)
Carry
\(\begin{array}{c@{}c@{}c@{}c@{}c} ^{1} & ^{1} & ^{1} & & \\ & 2 & 3 & 4 & 5 \\ + & 1 & 8 & 7 & 6 \\ \hline & & & & \\ \end{array}\)
Result
\(\begin{array}{c@{}c@{}c@{}c@{}c} ^{1} & ^{1} & ^{1} & & \\ & 2 & 3 & 4 & 5 \\ + & 1 & 8 & 7 & 6 \\ \hline 4 & 2 & 2 & 1 \\ \end{array}\)
Step 1: Align by place value

\(2,345 + 1,876\) → Write 2,345 above 1,876, aligning thousands, hundreds, tens, and ones columns

Step 2: Add the ones column

\(5 + 6 = 11\), write down 1 and carry 1 to the tens column

Step 3: Add the tens column with carry

\(4 + 7 + 1 = 12\), write down 2 and carry 1 to the hundreds column

Step 4: Add the hundreds column with carry

\(3 + 8 + 1 = 12\), write down 2 and carry 1 to the thousands column

Step 5: Add the thousands column with carry

\(2 + 1 + 1 = 4\), write down 4

\(2,345 + 1,876 = 4,221\)
Final answer:

\(2,345 + 1,876 = 4,221\)

Applied rules:

• Four-digit addition: Same process extends to thousands column

• Multiple carries: May need to carry in multiple columns simultaneously

• Place value: Each digit's position determines its value

Rules and methods, laws,...
\(24 + 38 = 62\)
Two-Digit Addition
Carrying Rule
If sum ≥ 10, carry 1 to next column
When adding digits results in 10 or more
Place Value
Ones, Tens, Hundreds, Thousands
Each position has specific value
Regrouping
Making groups of ten
Process of combining tens
Key definitions:

Place value: The value of a digit based on its position in the number

Carrying: Moving a group of ten from one column to the next

Regrouping: Reorganizing numbers into groups of tens, hundreds, etc.

Complete methodology:
  1. Align numbers: Place values in the same column (ones under ones, tens under tens...)
  2. Add from right to left: Start with the ones column
  3. Carry when needed: If sum is 10 or more, carry the extra to the next column
  4. Continue for all columns: Repeat for tens, hundreds, thousands, etc.
Tip 1: Always align numbers by place value before adding.
Tip 2: Remember to add any carried numbers to the next column.
Tip 3: Check your work by estimating before calculating.
Tip 4: Practice with smaller numbers first before moving to larger ones.
Common errors: Misaligning columns, forgetting to carry, adding carried numbers incorrectly.
Practice strategies: Use place value charts, draw lines to separate columns, check with estimation.
Formulas to know by heart:

• Carrying rule: When sum ≥ 10, carry 1 to the next column

• Place value: Each position has 10 times the value of the position to its right

• Addition algorithm: Add column by column from right to left

Add list of laws, methods, rules, definitions, expressions,.... Generate well SEO title for this section
\(24 + 38 = 62\)
Addition Algorithm
Ones Column
4 + 8 = 12 → Write 2, Carry 1
Always start here
Tens Column
2 + 3 + 1 = 6
Add carried amount
Final Result
62
Combine all columns
Essential Concepts:

Digit: Any of the symbols 0-9 used to make numbers

Place value: The value of a digit based on its position

Sum: The result of adding numbers together

Step-by-step Addition Process:
  1. Write vertically: Stack numbers with place values aligned
  2. Add rightmost column: Add digits in the ones place
  3. Carry if needed: If sum is 10 or more, write the ones digit and carry the tens digit
  4. Move left: Add the next column including any carried amounts
  5. Repeat: Continue for all columns
Tip 1: Use lined paper to keep columns straight.
Tip 2: Draw arrows to show where carries go.
Tip 3: Count out loud to track carried numbers.
Tip 4: Verify by subtracting one number from the sum to get the other.
Key insight: Addition is commutative (order doesn't matter) and associative (grouping doesn't matter).
Estimation: Round numbers before adding to check if your answer is reasonable.
Critical Rules for Addition:

• Alignment: Always align numbers by place value

• Direction: Add from right to left

• Carrying: When sum is 10 or more, carry the tens digit to the next column

• Verification: Estimate first to ensure your answer is reasonable

Questions & Answers

Question: I don't understand why I need to carry when adding multi-digit numbers. Why can't I just put the whole number in the column?

Answer: Great question! Carrying is essential because of our base-10 number system. Each place value can only hold one digit (0-9). When you add and get 10 or more, you have to "make a group of ten" and move it to the next higher place value.

Think of it like this: if you have 12 individual blocks, you can group 10 of them into a stick of 10, leaving 2 individual blocks. So you have 1 ten and 2 ones. That's why in the ones column, you write down the 2 and carry the 1 ten to the tens column.

Example: In 24 + 38, when you add 4 + 8 = 12, you can't fit 12 in the ones place. So you write down the 2 (the ones part) and carry the 1 (the tens part) to the tens column.

Question: My child keeps forgetting to add the carried number to the next column. What's the best way to help them remember?

Answer: This is a very common issue! Here are several strategies to help:

  • Visual marking: Have your child circle or highlight the carried number so it's more visible
  • Physical action: Have them tap or point to the carried number before adding the next column
  • Verbal reinforcement: Encourage them to say "plus the carried [number]" out loud
  • Color coding: Use a different colored pencil to write carried numbers

Another helpful tip is to have them add the carried number immediately to the next column before adding the original digits. For example, if carrying 1 to the tens column, they should mentally add that 1 to the tens digits first.

Question: Sometimes I have to carry in more than one column when adding big numbers. How do I keep track of all the carries?

Answer: It's completely normal to have multiple carries! Here's how to manage them:

  • Work systematically: Always move from right to left, one column at a time
  • Make carries visible: Write small numbers above the next column to show what you're carrying
  • Count carefully: When adding a column, count the original digits plus any carried numbers
  • Double-check: After completing each column, quickly verify your calculation

Remember, each carry represents a group of 10 that moves to the next higher place value. Don't worry about having multiple carries - just handle each column one at a time!