Problem 13 - Algebra A Combined Function

Question

Add or subtract as indicated. $$ 8.8-2.3 $$

Step-by-Step Solution

Answer

The result of subtracting 2.3 from 8.8 is 6.5.

Step 1: Understand the Operation

The problem requires subtracting two numbers, 8.8 and 2.3. This means we will take 2.3 away from 8.8.

Step 2: Align the Decimals

Write the numbers vertically, making sure to align the decimal points:\[\begin{array}{r} 8.8\-2.3\\hline\end{array}\]

Step 3: Subtract the Tenths

Subtract the fractional parts (right of the decimal). For the numbers 8.8 and 2.3, subtract 0.3 from 0.8, which gives 0.5.

Step 4: Subtract the Whole Numbers

Subtract the whole numbers, 8 and 2. Subtracting 2 from 8 gives 6.

Step 5: Combine the Results

Add the results from Step 3 and Step 4 together to get the final answer. Place the decimal point directly under the other decimal points:\[\begin{array}{r} 6.5\end{array}\]

Key Concepts

Understanding Decimals

Decimals are a way to represent numbers that are not whole, using a decimal point to separate the whole and fractional parts. They are particularly useful for precise calculations involving fractions of whole numbers.
For example, in the number 8.8, the '8' before the decimal point represents the whole part, while the '.8' signifies the fraction part, which is 8 tenths.
Understanding decimals involves getting familiar with the positions of digits after the decimal point. These positions are called tenths, hundredths, thousandths, etc., and they show the division of the whole into smaller parts.

• The first digit after the decimal point is called the tenths place.
• The second digit is called the hundredths place.
• The third digit is called the thousandths place, and so on.

Grasping the concept of decimals is essential as they are widely used in money, measurements, and scientific calculations.

Mastering Place Value

Place value is a fundamental concept in mathematics used to understand the value of each digit in a number. In our decimal system, each digit has a specific value based on its position.
To understand place value in decimals, consider the number 8.8.

• The '8' to the left of the decimal point represents "8 whole ones," while the '8' to the right of the decimal represents "8 tenths."
• This means 8.8 can be read as "eight and eight tenths."

The importance of place value lies in its ability to accurately describe the magnitude of the number. Without understanding place value, performing arithmetic operations on numbers, especially those including decimals, would be challenging.
When dealing with subtraction problems involving decimals, ensuring each digit's place is aligned correctly is crucial, as it guarantees proper subtraction of each component of the number.

Performing Basic Arithmetic Operations

Arithmetic operations are fundamental mathematical processes including addition, subtraction, multiplication, and division. Here we focus on subtraction, especially with decimals, as seen in the exercise.
Subtraction involves taking one number away from another to find the difference. When subtracting decimals, like 8.8 and 2.3, it is important to align the decimals vertically.

• Align the numbers so each digit is in the correct place value column, including the whole numbers and the fractional parts.
• Subtract each column starting from the rightmost side (tenths), then move to the left.
• It's crucial to subtract components of each place value separately to ensure accuracy.

In this example, we first subtracted the tenths, resulting in 0.5, then subtracted the whole numbers, resulting in 6. Finally, combine these results for the final answer of 6.5.
Understanding these steps is key to mastering subtraction involving decimals.