Problem 515 - Prealgebra

Question

Subtract and then check by adding. $$539-217$$

Step-by-Step Solution

Answer

The result of the subtraction is 322.

Step 1 - Subtract the Numbers

To subtract the numbers, start by writing them vertically, align the digits by place value: \[ \begin{array}{r} 539 \ -217 \ \hline \end{array} \] Now, subtract each column starting from the right:- Subtract the units place: \(9 - 7 = 2\)- Subtract the tens place: \(3 - 1 = 2\)- Subtract the hundreds place: \(5 - 2 = 3\)Thus, the result of the subtraction is \(322\).

Step 2 - Check by Adding

To check the subtraction, add \(322\) (the result) to \(217\) (the number subtracted) and see if the sum equals the original number: \[ \begin{array}{r} 322 \ +217 \ \hline \end{array} \]- Add the units place: \(2 + 7 = 9\)- Add the tens place: \(2 + 1 = 3\)- Add the hundreds place: \(3 + 2 = 5\)The sum is \(539\), which matches the original number. Hence, the subtraction was performed correctly.

Key Concepts

basic arithmetic

In basic arithmetic, learning to subtract and add numbers is fundamental. These operations are the building blocks for higher mathematical concepts. Whether you're subtracting or adding, the process involves handling digits in units, tens, hundreds, and so on.
Understanding these basics helps to enhance computational skills and forms the foundation for solving more complex problems down the line.
Let's explore these concepts more deeply to make sure you grasp them thoroughly.

subtracting numbers

When subtracting numbers, it's important to align the digits correctly by their place values: units, tens, hundreds, etc. This helps to keep the calculations organized and accurate. Let's revisit the example of subtracting 539 by 217:

1. Write the numbers one below the other with the digits lined up by place value:
\[ \begin{array}{r} 539 \ -217 \ \ \ \end{array} \]

2. Subtract each column starting from the right (units place).
\(9 - 7 = 2\text{ (units place)}\)
\(3 - 1 = 2\text{ (tens place)} \)
\(5 - 2 = 3\text{(hundreds place)} \)

As a result, we get 322. Each step ensures that every digit is subtracted from the correct position, providing an accurate answer.

addition for verification

After performing subtraction, it's good practice to verify the result by using addition. This step confirms the accuracy of your work. For the example 539 - 217 where our result was 322, we check it as follows:

1. Add the result of the subtraction (322) to the number that was subtracted (217):
\[ \begin{array}{r} 322 \ +217 \ \ \ \end{array} \]
2. Add each column starting from the right (units place): \(2 + 7 = 9\text{ (units place)} \)
\(2 + 1 = 3\text{ (tens place)} \)
\(3 + 2 = 5\text{(hundreds place)} \)

The sum is 539, which matches the original number. This confirms that the subtraction was done correctly. Always verify through addition to ensure the accuracy of your subtraction.

vertical alignment in subtraction

Vertical alignment of digits in subtraction is crucial for accurate calculations. It helps prevent errors that could occur if digits are misaligned. Let's break down why vertical alignment matters and how it works:

1. Write the numbers with each digit positioned directly below its counterpart of the same place value. This alignment ensures that units are subtracted from units, tens from tens, and so on.

2. Check the alignment carefully before you start subtracting. Misaligned digits can lead to incorrect results.
In our example:
\[ \begin{array}{r} 539 \ -217 \ \ \ \end{array} \]
3. Start from the rightmost column (units) and move leftward. This ensures no mistakes occur due to carry-over or borrowing, which can complicate subtraction.

Practicing proper vertical alignment helps develop good mathematical habits and ensures accurate calculations every time.