Problem 50 - Prealgebra

Question

Add and subtract as indicated. Subtract 8 from the sum of 9.37 and 2.5.

Step-by-Step Solution

Answer

The result is 3.87.

Step 1: Identify the Operations

The problem asks us to find the sum of 9.37 and 2.5 first, and then subtract 8 from this sum.

Step 2: Perform the Addition

Add 9.37 and 2.5 together. \[9.37 + 2.5 = 11.87\]The sum is 11.87.

Step 3: Perform the Subtraction

Now, subtract 8 from the result obtained in Step 2:\[11.87 - 8 = 3.87\]The result after subtraction is 3.87.

Key Concepts

Understanding Addition with Decimals

When adding decimal numbers, it's important to align the numbers by their decimal points. This ensures that each digit is correctly positioned according to its place value. Imagine stacking the numbers one on top of the other so that the tenths align with tenths, hundredths with hundredths, and so forth. For our exercise, we first add 9.37 and 2.5.

• The decimal point helps in categorizing the numbers into whole numbers and fractions of numbers.
• Adding: Just like with whole numbers, begin adding from the rightmost digit, and carry over if needed.
• When there are fewer digits, like 2.5 with a 'blank' hundredths place, consider it as 2.50 to make it easier to align vertically.

Using this approach, we find the sum to be 11.87, placing our focus on holding the decimal alignment to ensure precision in our calculation. In practice, double-check your alignment to prevent errors related to misplaced decimal points.

Mastering Subtraction with Decimals

Subtracting decimals requires a similar approach to aligning the numbers by their decimal points, ensuring that every digit is evenly matched up by their place value. The exercise calls for us to subtract 8 from 11.87. Here's how that works:

• Align the decimal in the number from which you are subtracting — here, it's 11.87.
• If subtracting a whole number, like 8, add a decimal point and zeroes to its right to match the decimal places of the number you're subtracting from, i.e., 8.00.
• Subtract digit by digit from right to left, borrowing from the next left column if necessary.

As we subtract, we're careful to maintain the decimal position straight down the line which results in 3.87. It reinforces how essential it is to keep an eye on these decimal points to ensure accuracy.

Step-by-Step Solutions Illustrate Clear Thinking

Working through math problems, especially involving decimals, benefits greatly from methodical, step-by-step solutions. This approach helps:

• Clarify the sequence of operations, ensuring each computation is distinctly understood.
• Offer tangible breaking points or checkpoints, where you can pause and verify accuracy before proceeding.
• Build confidence and reduce cognitive overload by focusing on one operation at a time.

In our original problem, breaking down the steps to first find the sum, and then perform the subtraction, not only aids in managing the process but also reveals the rationale behind each move. For a problem like subtracting 8 from the sum of 9.37 and 2.5, our step-by-step explanation yields clarity and drives home fundamental understanding in a structured way. Breaking down such problems reinforces understanding and provides a systematic way to tackle more complex arithmetic tasks in the future.