Problem 88 - Elementary Algebra

Question

Add or subtract and reduce to lowest terms. $$ 318-124 $$

Step-by-Step Solution

Answer

The result is 194.

Step 1: Understanding the Problem

We need to subtract 124 from 318 and then ensure that our final answer is reduced to its simplest form, though with whole numbers, reduction will not apply as it does for fractions.

Step 2: Perform the Subtraction

Subtract 124 from 318. Align the numbers by their place values. Starting from the rightmost digit, vertically subtract the corresponding digits. \(318 - 124 = 194\)

Step 3: Check Your Work

Verify the subtraction by adding the result back to the subtrahend to ensure it equals the minuend.\(194 + 124 = 318\)Since this calculation verifies our result, our subtraction was done correctly.

Key Concepts

Subtraction

Subtraction is one of the four basic arithmetic operations, where we calculate the difference between two numbers. To subtract correctly, it's essential to align the numbers according to their place values. When subtracting 124 from 318, start from the right, with the units, then tens, followed by the hundreds. This means you need to:

• Subtract the units place: 8 - 4 = 4.
• Subtract the tens place: 1 - 2. Since 1 is less than 2, you "borrow" 1 from the hundreds place, making it effectively 11 - 2 = 9.
• Subtract the hundreds place, after borrowing: 2 - 1 = 1.

Thus, 318 - 124 equals 194. Breaking down subtraction into these steps makes it easier to tackle complex calculations step-by-step.

Place Value

Place value is a core concept in arithmetic that helps us understand the value of digits based on their position in a number. In our subtraction example, each digit in 318 and 124 holds a specific place value, such as:

• 318: the 8 is in the units place, the 1 in the tens place, and the 3 in the hundreds place.
• 124: the 4 is in the units place, the 2 in the tens place, and the 1 in the hundreds place.

When numbers are arranged according to place value, it ensures accuracy in operations. During subtraction, aligning digits according to their place value allows for correct "borrowing" and ensures that you are subtracting equivalent positions, maintaining the accuracy of the results.

Verification of Results

Verification is an important part of any arithmetic operation, used to ensure that the result is correct. After performing subtraction, as seen with 318 - 124 = 194, verifying the result is crucial. One simple method for verifying subtraction is to reverse the operation:

• Take the result of the subtraction, in this case, 194.
• Add the subtracted number (subtrahend), which is 124, back to 194.
• If the sum equals the original number (minuend), the operation was done correctly. Here, 194 + 124 = 318.

Verification builds confidence in your arithmetic skills and ensures that what you calculated is indeed accurate. This process reinforces learning and prevents mistakes in further applications of subtraction.