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

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 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.

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 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, 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, 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, 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 follow these steps:

• Step 1: Align the numbers 2.5 and 3.1 by their decimal points.
• Step 2: Add the digits in each column starting from the rightmost digit (the tenths column in this case).

Now, let's work through each step:

Step 1: Align the numbers by decimal points:

$\phantom{00}2.5$
$+3.1$

Step 2: Perform the addition:
- Add the tenths column: $5 + 1 = 6$
- Add the units column: $2 + 3 = 5$

Therefore, by aligning and adding the numbers correctly, the solution to the problem is $5.6$.

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 this problem, we will perform the following steps:

• Step 1: Align the decimal numbers so the decimal points are vertically in line. The numbers are $10.1$ and $2.3$.
• Step 2: Add the numbers starting from the rightmost column (i.e., the tenths place), moving to the left.

Let's perform the addition:

$\begin{array}{c} 10.1 \\ + 2.3 \\ \hline \end{array}$

Starting from the right, we add the digits in the tenths place: $1 + 3 = 4$.

Next, add the digits in the units place: $0 + 2 = 2$.

Finally, add the digit in the tens place: $1 + 0 = 1$.

Therefore, the result of adding $10.1 + 2.3$ is:

$12.4$

We can verify that this matches with the given answer choices. The correct choice is:

Option 1: $12.4$