Question

\(34.56-13.23=\)

Short answer

21.33

Step-by-step solution

Align the Numbers

Write the numbers 34.56 and 13.23 with the decimal points aligned vertically.\[\begin{array}{r} 34.56 \-13.23 \end{array}\]

Subtract the Hundredths Place

Subtract the digits in the hundredths place: 6 - 3 = 3.\[\begin{array}{r} 34.56 \-13.23 \hline 0.03 \end{array}\]

Subtract the Tenths Place

Subtract the digits in the tenths place: 5 - 2 = 3.\[\begin{array}{r} 34.56 \-13.23 \hline 0.33 \end{array}\]

Subtract the Units Place

Subtract the digits in the units place: 4 - 3 = 1.\[\begin{array}{r} 34.56 \-13.23 \hline 1.33 \end{array}\]

Subtract the Tens Place

Subtract the digits in the tens place: 3 - 1 = 2.\[\begin{array}{r} 34.56 \-13.23 \hline 21.33 \end{array}\]

Write the Final Result

Combine all the results obtained in each step to form the final answer: 21.33.\[34.56 - 13.23 = 21.33\]

Key concepts

Aligning Decimal Points

When performing decimal subtraction, it's essential to align the decimal points of the numbers you are working with. This ensures that each place value, such as the tenths, hundredths, and units, lines up correctly.

For example, in the exercise given (\textbf{34.56 - 13.23}), start by writing the two numbers with their decimal points lined up vertically, like this:

\[ \begin{array}{r} 34.56 \-13.23 \ \ \ \ \end{array} \]

This will help you to clearly see which digits to subtract from each place value, streamlining the subtraction process. Make it a habit to always begin your decimal subtraction this way to avoid mistakes.

Place Value Subtraction

Understanding place value is crucial when subtracting decimals. Each digit represents a different place value (hundreds, tens, ones, tenths, hundredths). By subtracting one place value at a time, you can systematically find the correct answer.

Here's the breakdown for the exercise: 34.56 - 13.23:

• Hundredths Place: Subtract the digits in the hundredths place: 6 - 3 = 3.
\[ \begin{array}{r} 34.56 \-13.23 \hline \ 0.03 \end{array} \]

• Tenths Place: Subtract the digits in the tenths place: 5 - 2 = 3.
\[ \begin{array}{r} 34.56 \-13.23 \hline \ 0.33 \end{array} \]

• Units Place: Subtract the digits in the units place: 4 - 3 = 1.
\[ \begin{array}{r} 34.56 \-13.23 \hline 1.33 \end{array} \]

• Tens Place: Subtract the digits in the tens place: 3 - 1 = 2.
\[ \begin{array}{r} 34.56 \-13.23 \hline 21.33 \end{array} \]

Finally, by combining all the results, the final answer is 21.33.

Breaking it down this way ensures you maintain accuracy at each step.

Step-by-Step Problem Solving

Solving math problems step-by-step helps you organize your thoughts and actions clearly. It also allows for easier identification of any mistakes.

Let's review the steps for solving the given exercise (34.56 - 13.23).

• Step 1: Align the Numbers
Align the decimals vertically.


• Step 2: Subtract the Hundredths Place
Subtract the digits in the hundredths place: 6 - 3 = 3.


• Step 3: Subtract the Tenths Place
Subtract the digits in the tenths place: 5 - 2 = 3.


• Step 4: Subtract the Units Place
Subtract the digits in the units place: 4 - 3 = 1.


• Step 5: Subtract the Tens Place
Subtract the digits in the tens place: 3 - 1 = 2.


• Step 6: Write the Final Result
Combine the numbers from each place value for the final result: 21.33.


Each step builds upon the previous one, making the process logical and manageable. By practicing this method, it will become second nature to you.