Problem 16 - Algebra A Combined Function

Question

Add or subtract as indicated. $$ 28-3.31 $$

Step-by-Step Solution

Answer

The result is 24.69.

Step 1: Identify Operation

The problem presents the expression \(28 - 3.31\). This indicates that subtraction is needed.

Step 2: Align the Numbers

Align the numbers vertically, keeping decimals in line:\[ \begin{array}{r} 28.00 \ - 3.31 \ \hline \end{array}\]

Step 3: Perform Subtraction

Subtract beginning from the rightmost digit to left.1. Subtract 1 from 0: Must borrow from the hundredths place: - \(10 - 1 = 9\).2. Subtract 3 from 9 (after borrowing): - \(9 - 3 = 6\).3. Subtract 3 from 8: - \(8 - 3 = 5\).4. Subtract 0 from 2: - \(2 - 0 = 2\).Combine to get the final answer: \(24.69\).

Step 4: Check Your Work

Re-adding the result with the subtracted value gives the original number:\(24.69 + 3.31 = 28.00\). This confirms the subtraction is correct.

Key Concepts

Subtraction

Subtraction is one of the four basic arithmetic operations. It is the process of taking one number away from another. In the context of problems like \(28 - 3.31\), subtraction involves finding the difference between two numbers.
When performing subtraction, it's essential to line up the numbers correctly, especially when they include decimals. Start from the rightmost digit and move to the left.

• Look out for cases where borrowing is necessary. If the digit in the top number is smaller than the bottom number, you need to borrow from the next left digit.
• This "borrowing" step can be tricky but is crucial for getting the correct answer. Make sure to adjust your top number accordingly and repeat the subtraction process.

Subtraction can be straightforward when you are dealing with whole numbers, but it requires more attention when decimals are involved. By practicing regularly, you can become more confident in solving subtraction problems.

Decimal Subtraction

Decimal subtraction works similarly to whole number subtraction but requires a few additional considerations.
When subtracting numbers like \(28 - 3.31\), it’s important to:

• Align the decimal points to ensure the correct placement of each digit.
• Fill in any blank spaces with zeros to maintain a consistent column alignment.

For decimal subtraction, the same principles apply as when dealing with whole numbers. If the top digit is smaller than the bottom one, borrowing is necessary. Be sure to:

• Borrow from the next left digit, and replace the borrowed spot with a zero.
• Check your work by adding the result to the number subtracted; the sum should be the original number before subtraction.

This practice of checking your work ensures accuracy and helps reinforce the learned concepts.

Mathematics Education

Mathematics education provides students with essential skills for everyday calculations and problem-solving. Subtraction and decimal subtraction are fundamental parts of this education.
Understanding subtraction's role in mathematics helps build a foundation for more advanced topics. By fostering a solid grasp of basic arithmetic, students gain confidence that translates into better performance in many subjects. To enhance learning:

• Reinforce concepts with practical examples students can relate to.
• Encourage practice through exercises that gradually increase in difficulty.
• Provide clear, step-by-step explanations to prevent misunderstandings.

Education in mathematics is not just about getting the right answer; it's about understanding why the answer is correct. Exploring diverse methods and providing hands-on experiences can lead to deeper comprehension and a greater appreciation of math in everyday life.