Problem 14 - Algebra A Combined Function

Question

Add or subtract as indicated. $$ 7.6-2.1 $$

Step-by-Step Solution

Answer

7.6 - 2.1 = 5.5

Step 1: Identify the Operation

The problem asks us to subtract 2.1 from 7.6. Hence, we are dealing with a subtraction operation.

Step 2: Align Decimal Points and Subtract

Write both numbers one below the other, aligning the decimal points:\[\begin{array}{r} 7.6 \- 2.1 \\hlinedots\end{array}\]Subtract each digit starting from the right (tenths place in this case).

Step 3: Perform the Subtraction

Subtract the tenths: 6 - 1 = 5.Subtract the units (ones): 7 - 2 = 5.Combine these results to get the final answer:\[7.6 - 2.1 = 5.5\]

Key Concepts

Step-by-Step Subtraction

Step-by-step subtraction is a methodical approach that helps us accurately solve subtraction problems, especially when dealing with more than simple whole numbers. The first step in any subtraction problem is to identify what numbers we need to subtract. In this example, we need to subtract 2.1 from 7.6.
The method involves a few clear steps:

• Identify the operation: Determine that you are performing a subtraction operation.
• Align the numbers: Make sure that decimal points are lined up correctly.
• Subtract each place value: Start subtracting from the rightmost digits, moving left.

Following these steps ensures each part of the number is subtracted logically and clearly, making the process straightforward.

Aligning Decimal Points

Aligning decimal points is crucial in the subtraction of decimals. This ensures that numbers are correctly positioned according to their place values—units with units, tenths with tenths, hundredths with hundredths, and so on.
When you first write the numbers, make sure the decimal points form a straight, vertical line. This alignment allows you to clearly see which digits need to be subtracted from each other.

• Write numbers one below the other with decimal points fully aligned.
• Fill in any missing place values with zeros to make the subtraction process easier.

Aligning decimal points prevents mistakes and makes subtraction of decimals as easy as subtracting whole numbers.

Subtracting Decimals

Subtracting decimals follows the same rules as subtracting whole numbers, once the decimal points are aligned. Start from the rightmost digits, which usually represent the smallest place value.
In our specific example of subtracting 2.1 from 7.6:

• Subtract the tenths: Look at the tenths place under each aligned decimal point. Subtract 1 from 6 to get 5.
• Move to the units: Then, move to the units place. Subtract 2 from 7 to also get 5.
• Write down the result: Combine results from all place values. Here we have 5 in the units place and 5 in the tenths place, resulting in 5.5.

Understanding these steps is crucial to getting the correct answer when subtracting decimals.