Problem 64 - Algebra 1: Concepts and Skills

Question

Subtract. $$ 11.9-1.2 $$

Step-by-Step Solution

Answer

The difference of 11.9 and 1.2 is 10.7

Step 1: Alignment

The first step is to align the numbers by their decimal points. This makes the subtraction process clearer. Written vertically, this would look like: \[\begin{align*} &11.9\ -&1.2\ \end{align*}\]

Step 2: Subtraction

In the next step, the subtraction is done from right to left. Starting from the tenths place, subtract the bottom number from the top number: \(9-2=7\). Then, move to the units place and do the same: \(1-1=0\). Finally, bring down any remaining numbers: \(1\).

Step 3: Final Answer

Write the final answer as \(10.7\), obtained from combining the results from the units and tenths places.

Key Concepts

Aligning Decimal Points

When performing decimal subtraction, it's crucial to line up the numbers correctly by their decimal points. This helps ensure that each digit is in the proper column. So, if you have numbers like 11.9 and 1.2, it's essential to write them one above the other, aligning the decimal points directly. Aligning in this way will make the subtraction reliable, and you'll avoid errors that can happen when digits are misplaced. Always ensure that decimal points are lined up for hassle-free calculation.

Subtraction Process

Once the decimal points are aligned, the subtraction process can begin. Subtraction should be done from right to left, just like regular subtraction. Begin with the smallest place value visible: the tenths place. Carefully subtract the digits column by column.

Here is a simple way to approach it:

• Start at the tenths place on the right and subtract: If you have 9 tenths minus 2 tenths, you get 7 tenths.
• Move to the units or ones place next.
• Continue the process left until all digits have been subtracted.

Throughout this step, be careful of any potential need for "borrowing" from the next column if a smaller digit subtracts a larger one. However, in our example, borrowing is not required.

Tenths Place

The tenths place is the first step in the subtraction process of this example. It refers to the digits immediately following the decimal point. When subtracting numbers, focus on this place first to simplify the calculation process.

In our example:

• The digit in the tenths place of 11.9 is 9.
• The corresponding digit in the tenths place of 1.2 is 2.

Subtract these digits: 9 tenths minus 2 tenths equals 7 tenths. Be sure to write this result in the tenths place below the line in your calculation. This strategy demonstrates clarity and precision in decimal subtraction.

Units Place

The units place, also known as the ones place, is before the decimal and is usually the easiest place to subtract. In the exercise example:

• The units digit in 11.9 is 1.
• The units digit in 1.2 is also 1.

Since both digits are the same, subtracting gives us zero. Thus, nothing remains in the units place.

After completing all the subtraction, combine the results from each place to write the final answer: 10.7. This simple approach ensures accurate decimal subtraction and reinforces the understanding of place values in mathematics.