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.

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.

Let's solve the problem step by step:

• Step 1: Align the numbers by their decimal points:
  $\begin{array}{c} 5.7 \\ - 2.3 \\ \hline \end{array}$
• Step 2: Subtract the digits in the tenths place $7 - 3 = 4$.
• Step 3: Subtract the digits in the units place $5 - 2 = 3$.
• Step 4: Write down the result by combining both differences, making sure to keep the decimal point aligned: $3.4$.

Therefore, the solution to the problem is $3.4$.

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.

To solve the addition problem $4.3 + 6.2$, follow these steps:

• Step 1: Align the numbers by their decimal points as follows:
       $4.3$
  $+\,6.2$
  
• Step 2: Add the digits to the right of the decimal point first:
       $3 + 2 = 5$
• Step 3: Add the digits to the left of the decimal point:
       $4 + 6 = 10$

Now, place the decimal point in the result directly below the other decimal points:

$4.3 + 6.2 = 10.5$

Therefore, the solution to the problem is $10.5$.

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 the subtraction problem $7.9 - 5.3$, we will follow a simple step-by-step process:

• Step 1: Align the decimal points of both numbers. Write $7.9$ directly above $5.3$ such that the decimal points are lined up vertically.

• Step 2: Perform the subtraction from right to left. Start with the tenths place:
  Subtract $3$ (from 5.3) from $9$ (from 7.9) in the tenths place, resulting in $6$.

• Step 3: Move to the units place:
  Subtract $5$ (from 5.3) from $7$ (from 7.9) in the units place, resulting in $2$.

After subtracting, we find the result of the operation $7.9 - 5.3$ is $2.6$.

Therefore, the solution to the problem is$2.6$.

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, let's follow these steps for decimal addition:

• Step 1: Align the decimals of the numbers vertically, so that both $5.1$ and $2.3$ have their decimal points in the same position:

   5.1
+  2.3
---------

• Step 2: Start adding from the rightmost column (the tenths position). Add the tenths: $1 + 3 = 4$.
• Step 3: Move to the left to add the units: $5 + 2 = 7$.

Put these sums together, and we have:

   5.1
+  2.3
---------
   7.4

Therefore, the sum of $5.1$ and $2.3$ is $7.4$. This matches choice $\text{3}$.

Thus, the correct answer is $7.4$.

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 problem, let's perform the following steps:

• Step 1: Write the numbers vertically, aligning the decimal points.
• Step 2: Subtract as you would with whole numbers, starting from the right.
• Step 3: Bring down the decimal point in the same position below the numbers being subtracted.

Now, applying these steps to $0.4 - 0.2$:

• 0.4
• − 0.2

So, the result of $0.4 - 0.2$ is $0.2$.

In this problem, the correct answer from the provided choices is 0.2.

To solve this problem, we follow these steps:

• Step 1: Write down the numbers vertically, aligning the decimal points.
• Step 2: Add each column of digits, starting from the rightmost column (the tenths place).
• Step 3: If any column adds to a number equal to or greater than 10, carry over to the next left column.

Let's work through the solution:
Step 1: Align the numbers vertically:
    6.2
+ 2.4
--------
Step 2: Add the digits in the tenths column: $2 + 4 = 6$. Write the 6 in the tenths place below.
Step 3: Add the digits in the ones column: $6 + 2 = 8$. Write the 8 in the ones place below.
Therefore, the sum of $6.2$ and $2.4$ is $8.6$.

Therefore, the solution to the problem is $8.6$, which corresponds to choice 1.

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 $\mathbf{30.8}$.