Addition and Subtraction of Decimal Fractions - Examples, Exercises and Solutions

First let's fill in the zeros in the empty spaces as follows:

$21.52\\+03.40\\$Note that the decimal points are written one below the other.

Therefore, the positions of the decimal points correspond and thus the exercise is written in the correct form.

Note that the decimal points are not written one below the other. They do not correspond.

Therefore, the exercise is not written correctly.

Note that the decimal points are not written one below the other. They do not correspond.

Therefore, the exercise is not written correctly.

To determine if the addition problem is set up correctly, we need to analyze how the numbers are aligned.

The given numbers for addition are $312.54$ and $1203.22$. When aligning these numbers for addition:

$\begin{array}{r} 312.54 \\ +1203.22 \\ \hline \end{array}$

We examine how the decimal points are positioned. For a correct setup, the decimal points should be aligned vertically. However, in the visual provided:

• The decimal point in $312.54$ is positioned one place to the right compared to the decimal in $1203.22$.

• The alignment should have appeared as $\begin{aligned} &\phantom{00}312.54 \\ &+1203.22 \end{aligned}$ to be correct, but it does not.

Since the decimal points are not vertically aligned, the addition is set up incorrectly.

Therefore, the statement regarding the positioning of the decimal points is Not true.

First let's fill the zeros in the empty space as follows:

$006.310\\+216.222\\\$

Here We should note that the decimal points are written one below the other.

Therefore, the exercise is written in the appropriate form.

To solve this problem, we will follow these steps:

• Step 1: Align the decimal points of the numbers to be added.
• Step 2: Add the numbers directly using their place values.
• Step 3: Write down the sum.

Now, let's perform each step in detail:

Step 1: Align the decimal points of $0.1$ and $0.1$.

Step 2: Add the tenths place values. Since both digits in the tenths place are $1$, we add them together:

$1 + 1 = 2$

Step 3: Write down the sum with the decimal point aligned:

The sum is $0.2$.

Therefore, the solution to the problem is $0.2$.

To solve this problem, we need to add the decimal numbers $0.2$ and $0.1$.

Here are the steps to perform the addition:

• Step 1: Align the numbers by their decimal points:
      $0.2$
  + $0.1$
• Step 2: Start adding from the rightmost digit to the left:
• The tenths column contains 2 tenths (from $0.2$) and 1 tenth (from $0.1$), and adding these gives 3 tenths. There is no carryover since the result is below 10 tenths.
• The single whole number place doesn't have digits to sum aside from the carry, which in this case, is zero.
• Step 3: The sum of $0.2 + 0.1$ is $0.3$.

Therefore, the solution to the problem is $0.3$.

To solve this problem, let's follow these steps:

• Step 1: Identify the decimal numbers involved, which are $0.2$ and $0.1$.
• Step 2: Align the decimal points for the numbers vertically and perform the subtraction.

Now, let's proceed with the calculation:

$0.2 - 0.1 = 0.1$ The operation involves subtracting $0.1$ from $0.2$ by aligning the decimal points. Since both numbers have only one decimal place, the decimals align easily, making the subtraction straightforward.

Therefore, the result of the subtraction
$0.2 - 0.1$ is $0.1$.

The correct choice from the given options is Choice 2: $0.1$.

To solve this subtraction problem effectively, we can follow a clear method of subtracting decimal numbers:

• Step 1: Align the decimal numbers vertically by their decimal points.
• Step 2: Write the numbers as:
  $\begin{array}{c} \\ 0.3\\ -0.2\\ \hline \end{array}$
• Step 3: Subtract the digits from right to left. Here, we only have the tenths place to consider.
• Subtract $2$ tenths from $3$ tenths: $3 - 2 = 1$.
• Step 4: The result of the subtraction is $0.1$.

Thus, the result of the subtraction $0.3 - 0.2$ is $0.1$.

To solve this problem, we'll follow these steps:

• Step 1: Align the decimal points vertically in the numbers to be added.
• Step 2: Add the numbers as if they were whole numbers, placing the decimal correctly in the sum.

Let's perform the addition:

Step 1: Align the numbers $0.4$ and $0.4$: $\begin{array}{c} \phantom{+}0.4 \\ + 0.4 \\ \hline \end{array}$

Step 2: Add $4$ and $4$ in the tenths place, which gives us $8$. The decimal point remains in the same position, resulting in $0.8$.

Therefore, the sum of $0.4 + 0.4$ is $0.8$.

To solve this problem, follow these steps:

• Step 1: Align the numbers vertically by their decimal point. Write $0.5$ and $0.3$ ensuring the decimal points are aligned.
• Step 2: Perform the addition:
        0.5
  +    0.3
  —---------
• Step 3: Add the numbers starting from the right (tenths place):
  - Add $0.5 + 0.3 = 0.8$.

Therefore, the sum of $0.5$ and $0.3$ is $0.8$.

To solve this problem, we will perform the subtraction of two decimal numbers, $0.5$ and $0.3$.

• Align the numbers by their decimal points:

  $0.5$

  $-0.3$

• Since the numbers are already aligned, subtract the tenths digit of $0.3$ from the tenths digit of $0.5$:

  $5 - 3 = 2$

• Place this result in the tenths position of the answer, resulting in

  $0.2$.

The subtraction of $0.3$ from $0.5$ results in

$0.2$.

To solve this problem, we will add the decimal numbers 0.75 and 0.35 by aligning them according to their decimal points:

• Step 1: Align the numbers vertically by their decimal points:

  $\begin{array}{c} \phantom{0}\\ \phantom{0} \quad 0.75 \\ + \quad 0.35 \\ \hline \end{array}$

• Step 2: Add the digits starting from the rightmost column (hundredths place):

  - Hundredths place: $5 + 5 = 10$. Write 0 and carry over 1 to the tenths place.
  - Tenths place: $7 + 3 + 1 = 11$. Write 1 and carry over 1 to the units place.
  - Units place: $0 + 0 + 1 = 1$.

• Step 3: Write the final sum by placing the decimal point correctly below the decimal points of the addends:

  $\begin{array}{c} 0.75\\ + 0.35\\ \hline 1.10\\ \end{array}$

The sum of 0.75 and 0.35 is therefore $\textbf{1.10}$, which can be simplified to $\textbf{1.1}$ by removing the trailing zero after the decimal point.

The correct answer is, therefore, $\textbf{1.1}$, corresponding to choice $3$.

To solve the problem $15.8 - 3.5$, we will perform decimal subtraction:

• Step 1: Align the decimal places.
  Write the numbers so their decimal points are lined up:
  $\quad 15.8\\ - \, 3.5\\ --------$
• Step 2: Subtract the numbers column by column.
  - Start from the rightmost digit (tenths place), $8 - 5 = 3$. Write $3$ under the line in the tenths place.
  - Move to the next left column (ones place), $5 - 3 = 2$. Write $2$ in the ones place.
  - The digit in the tens place $1$ moves straight down as there is no number to subtract from.
  $\quad 15.8\\ - \, 3.5\\ \underline{--------}\\ \quad 12.3$
• Step 3: Conclude with the final answer.
  The result of $15.8 - 3.5$ is $12.3$.

Therefore, the correct answer is: $12.3$.

To solve this problem, we'll add the decimal numbers $20.4$ and $10.4$ by aligning the decimal points:

• Step 1: Write the numbers in a column aligning their decimal points:

$\begin{array}{r} 20.4 \\ +10.4 \\ \hline \end{array}$

• Step 2: Add the numbers starting from the right. First, $4 + 4 = 8$.
• Next, add the digits to the left of the decimal point: $0 + 0 = 0$.
• Finally, add the leftmost digits: $2 + 1 = 3$.

Combining these, the result is $30.8$.

Thus, the solution to the problem is $\mathbf{30.8}$.