Addition and Subtraction of Decimal Fractions: Simple addition adding 0

To solve this problem, follow these steps:

• Identify the given numbers: $5.3$ and $2.45$.
• Align them by the decimal point:

  5.30
+ 2.45
------

Note that adding a zero to the right of $5.3$ makes it $5.30$, which does not change its value but ensures alignment.

Next, perform the addition starting from the rightmost digit:

• Hundredths place: $0 + 5 = 5$
• Tenths place: $3 + 4 = 7$
• Units place: $5 + 2 = 7$

Thus, the sum is:

  5.30
+ 2.45
------
  7.75

The sum of $5.3$ and $2.45$ is $7.75$.

Therefore, the correct choice corresponding to our solution is choice 1: $7.75$.

To find the sum of $2.16$ and $3.214$, follow these steps:

• First, write the numbers vertically, aligning them by their decimal points:

$\phantom{00}2.160$
$+3.214$
$\_\_\_\_\_\_$

• Add the numbers from right to left, adding zeros if necessary to balance the number of decimal places:

• Start from the rightmost digit: $0 + 4 = 4$.

• Next column to the left: $6 + 1 = 7$.

• Next column to the left: $1 + 2 = 3$.

• Finally, add the whole number part: $2 + 3 = 5$.

• Combine the results to get the final sum.

Therefore, the sum of $2.16$ and $3.214$ is $\textbf{5.374}$.

To solve this problem, we'll add the numbers 100 and 10.3.

Let's break down the steps as follows:

• Step 1: Align the numbers vertically by the decimal point. While $100$ is a whole number, it can be written as $100.0$ to facilitate alignment. Therefore, write the numbers as: $\begin{array}{r} 100.0 \\ + 10.3 \\ \hline \end{array}$
• Step 2: Proceed with addition, starting from the rightmost digits. The setup allows addition digit-by-digit:
• Add the tenths place: $0 + 3 = 3$.
• Add the ones place: $0 + 0 = 0$.
• Add the tens place: $0 + 1 = 1$.
• Add the hundreds place: since there's nothing above the 1, it remains $1$.
• Step 3: Carefully maintain the decimal position. The result of this addition will be $110.3$.

Therefore, the sum of $100 + 10.3$ is $110.3$.

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

• Step 1: Align the numbers based on the decimal point.
• Step 2: Perform addition starting from the rightmost digit, carrying over as necessary.
• Step 3: Ensure the decimal point is placed correctly in the final answer.

Now, let's work through each step:

Step 1: Align the numbers vertically:

  6.40
+ 2.56
------

Step 2: Start with the hundredths place (rightmost) and move left.

• Add the hundredths: $0 + 6 = 6$.
• Add the tenths: $4 + 5 = 9$.
• Add the units: $6 + 2 = 8$.

Step 3: Place the decimal point directly below the other decimal points in the final answer.

  6.40
+ 2.56
------
  8.96

Therefore, the solution to the problem is $8.96$.

To solve this problem, follow these steps:

• Step 1: Recognize the numbers to be added are $3$ and $4.57$.

• Step 2: Write $3$ as $3.00$ for easier alignment by the decimal point.

• Step 3: Align the numbers:
        $\phantom{0}3.00$
  $+4.57$

• Step 4: Add the numbers column by column starting from the rightmost column.

Let's perform the addition:

• Rightmost column (hundredths): $0 + 7 = 7$.

• Next column (tenths): $0 + 5 = 5$.

• Next column (units): $3 + 4 = 7$.

The sum of $3$ and $4.57$ is calculated as follows:

First, verify the alignment of the decimals, then add each column:

$3.00 + 4.57 = 7.57$

The calculated sum is $7.57$.

The correct answer from the given choices is: $7.57$, which matches choice 3.