Problem 490
Question
Add. $$63+29$$
Step-by-Step Solution
Verified Answer
92
1Step 1: Write down the numbers
Write the numbers in a column, aligning them by their place values: \[ \begin{array}{c} 63 \ + \, 29 \ \bigstrut \ \ \ \ \ \end{array} \]
2Step 2: Add the ones place
Add the digits in the ones place (3 from 63 and 9 from 29). \[ 3 + 9 = 12 \] Write down 2 in the ones place and carry over the 1 to the tens place.
3Step 3: Add the tens place with carry
Add the digits in the tens place (6 from 63 and 2 from 29) including the carry-over 1. \[ 6 + 2 + 1 = 9 \] Write down 9 in the tens place.
4Step 4: Combine the results
Combine the digits in the tens and ones place to get the final answer: \[ 92 \]
Key Concepts
Place ValueCarrying in AdditionStep-by-Step Addition
Place Value
Understanding place value is very important in addition. Place value tells us the value of each digit in a number based on its position. The rightmost digit is in the 'ones' place, the next is in the 'tens' place, followed by the 'hundreds' place, and so on.
For example, in the number 63:
\(6\) is in the tens place and represents \(60\) (which is \(6 \times 10\)).
\(3\) is in the ones place and represents \(3\) (which is \(3 \times 1\)).
It's important to align the numbers by their place values when adding or subtracting to ensure that digits from the same place value are combined correctly. This alignment helps prevent mistakes.
For example, in the number 63:
\(6\) is in the tens place and represents \(60\) (which is \(6 \times 10\)).
\(3\) is in the ones place and represents \(3\) (which is \(3 \times 1\)).
It's important to align the numbers by their place values when adding or subtracting to ensure that digits from the same place value are combined correctly. This alignment helps prevent mistakes.
Carrying in Addition
Carrying in addition happens when the sum of digits in a place value exceeds 9. This is also called 'regrouping' or 'borrowing.'
For instance, in our example of adding \(63+29\):
When we add the ones place digits, \(3 + 9\), we get \(12\). We write down \(2\) in the ones place because \(12\) is actually \(1\times 10 + 2\). We carry over the \(1\) to the tens place.
Next, we add the tens place digits, considering our carry-over:\(6 + 2 + 1\), which gives \(9\).
This way, carrying ensures accuracy in addition, particularly for larger numbers. It may seem difficult at first, but with practice, it becomes an easy technique.
For instance, in our example of adding \(63+29\):
When we add the ones place digits, \(3 + 9\), we get \(12\). We write down \(2\) in the ones place because \(12\) is actually \(1\times 10 + 2\). We carry over the \(1\) to the tens place.
Next, we add the tens place digits, considering our carry-over:\(6 + 2 + 1\), which gives \(9\).
This way, carrying ensures accuracy in addition, particularly for larger numbers. It may seem difficult at first, but with practice, it becomes an easy technique.
Step-by-Step Addition
Breaking down addition into simple steps makes it easier to understand and perform correctly.
Here is a step-by-step guide using the problem \(63 + 29\):
Here is a step-by-step guide using the problem \(63 + 29\):
- Step 1: Write the numbers in a column aligning their place values.
\(\begin{array}{c} 63 \ + 29 \ \bigstrut \ \ \end{array} \) - Step 2: Add the ones place digits (3 from 63 and 9 from 29).
\(3 + 9 = 12\)
Write down \(2\) in the ones place and carry over the \(1\) to the tens place. - Step 3: Add the tens place digits, including the carry-over \(1\).
\(6 + 2 + 1 = 9\)
Write down \(9\) in the tens place. - Step 4: Combine the digits from the tens and ones places to form the final answer: \(92\).