Questions and Answers
The standard algorithm for multi-digit addition is also known as the ______ method.
column addition
In the standard algorithm, you add each column starting from the ______ place.
right
When the sum of a column is greater than or equal to 10, you need to ______ the extra digit to the next column.
carry
Understanding the value of each digit in a number based on its position is known as ______ value.
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In multi-digit addition, ______ occurs when the sum of a column is greater than or equal to 10.
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The final step in the standard algorithm is to ______ the final answer.
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Study Notes
Multi-Digit Addition
Standard Algorithm
- Also known as the column addition method
- Steps:
- Line up the numbers correctly, with the corresponding place values in the same column
- Add each column starting from the right (ones place)
- If the sum of a column is greater than or equal to 10, carry the extra digit to the next column
- Repeat step 2 and 3 until all columns have been added
- Write the final answer
Key Concepts
- Place value: understanding the value of each digit in a number based on its position (ones, tens, hundreds, etc.)
- Regrouping: when the sum of a column is greater than or equal to 10, carrying the extra digit to the next column
- Carrying: adding the regrouped digit to the next column
Examples
- 2-digit addition:
- 45 + 27 =
- Line up numbers: 45, 27
- Add ones place: 5 + 7 = 12, write 2, carry 1
- Add tens place: 4 + 2 + 1 (carried) = 7
- Final answer: 72
- 45 + 27 =
- 3-digit addition:
- 247 + 135 =
- Line up numbers: 247, 135
- Add ones place: 7 + 5 = 12, write 2, carry 1
- Add tens place: 4 + 3 + 1 (carried) = 8
- Add hundreds place: 2 + 1 = 3
- Final answer: 382
- 247 + 135 =
Multi-Digit Addition
Standard Algorithm
- The standard algorithm for multi-digit addition is also known as the column addition method.
- It involves lining up numbers correctly with corresponding place values in the same column.
- The algorithm starts by adding each column from the right (ones place).
- If the sum of a column is ≥ 10, the extra digit is carried to the next column.
- Steps 2 and 3 are repeated until all columns have been added.
- The final answer is written after completing all the steps.
Key Concepts
- Place value is the value of each digit in a number based on its position (ones, tens, hundreds, etc.).
- Regrouping occurs when the sum of a column is ≥ 10, requiring the extra digit to be carried to the next column.
- Carrying involves adding the regrouped digit to the next column.
Understanding the Algorithm
- Line up numbers correctly with corresponding place values in the same column.
- Always start adding from the right (ones place).
- Carry extra digits (≥ 10) to the next column.
- Repeat the process until all columns have been added.
- Write the final answer after completing all the steps.
Examples
- 2-digit addition: understanding place value and regrouping.
- 3-digit addition: applying the standard algorithm to add numbers with hundreds place.
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Description
Learn the steps to add multi-digit numbers using the standard algorithm, including understanding place values and carrying digits. Test your skills with this quiz!
