Addition and Subtraction of Decimal Fractions: Graphical representation - addition with regrouping

To solve the problem, let's add the decimals 0.7 and 0.8:

• Step 1: Align the numbers by their decimal points:
• $0.7$
• $+0.8$
• Step 2: Add the digits from right to left:
• Tenths place: $7 + 8 = 15$

The result of $7 + 8$ gives $15$. Since we are in the tenths column, the value is 1.5 (carrying the 1 over to the units place). Thus, the sum is $1.5$.

Therefore, the solution to the problem is $\boxed{1.5}$.

To solve the problem of adding $0.5$ and $0.9$, we follow these steps:

• Step 1: Write the numbers vertically and align the decimal points:

$\begin{array}{c} 0.5 \\ +0.9 \\ \hline \end{array}$

• Step 2: Add the numbers starting from the rightmost digit:

The digit after the decimal in $0.5$ is $5$, and in $0.9$ it is $9$.
Adding these, $5 + 9 = 14$. Write down $4$ and carry over $1$.

• Step 3: Add the numbers before the decimal point with the carryover:

Since $0.5$ has $0$ and $0.9$ has $0$ before the decimal, add these along with the carryover. $0 + 0 + 1 = 1$

Thus, when we perform the addition, we find the result is $1.4$.

Therefore, the solution to the problem is $1.4$.

To solve the problem $0.6 + 0.7$, we'll perform simple addition of decimal numbers:

• Step 1: Align the numbers by their decimal points:
  0.6
  + 0.7
• Step 2: Add the numbers column by column, starting from the rightmost digit:

0.6 can be thought of as 0.60 if we want to align them neatly:
0.60
+ 0.70
---------------

• Add the hundredths (rightmost) digit: 0 + 0 = 0
• Add the tenths digit: 6 + 7 = 13. Since this sum is greater than 9, we write down 3 and carry over 1 to the ones column.
• Add the digits in the ones column: 0 + 0 = 0, then add the carried over 1 to get 1.

The result of the addition $0.6 + 0.7$ is $1.3$. This matches our expectations from the arithmetic process.

Therefore, the solution to the problem is $1.3$.

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

• Step 1: Align the numbers by their decimal points.
  Write $0.6$ directly under $0.6$:
$\begin{array}{c} 0.6 \\ +0.6 \end{array}$
• Step 2: Add the tenths places. $6 + 6 = 12$. Write down $2$ in the tenths place and carry over $1$ to the units place.
• Step 3: Add the units place with the carry-over. $0 + 0 + 1 = 1$. Write down $1$ in the whole number place.

Thus, when we add $0.6$ and $0.6$, we obtain:

$1.2$

Therefore, the solution to the problem is $1.2$.

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

• Step 1: Align the numbers by their decimal points.
• Step 2: Add the numbers starting from the furthest right decimal place.
• Step 3: Handle any carryover if necessary.

Let's apply these steps to our problem:

Step 1: We align $0.9$ and $0.8$ so that their decimal points are in a column:
$\begin{array}{c} 0.9 \\ +0.8 \\ \hline \end{array}$

Step 2: Add the numbers starting from the rightmost digit (tenths place):
- In the tenths place, $9 + 8 = 17$. This results in $7$ in the tenths place and carry $1$ to the units place.

Step 3: Handle the carryover:
- In the units place, we consider any carry. Adding the carry $1$ from the tenths place gives us $1 + (0 + 0) = 1$.

So, the final result after addition is:
$\begin{array}{c} 1.7 \\ \end{array}$

Therefore, the sum of $0.9$ and $0.8$ is $\boxed{1.7}$.

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

• Step 1: Align the numbers $0.6$ and $0.5$ by their decimal points.
• Step 2: Add the numbers as you would do with whole numbers.
• Step 3: Place the decimal point in the sum directly under the decimal points of the addends.

Now, let's work through each step:
Step 1: Write the numbers aligned by the decimal point:
0.6
+ 0.5
Step 2: Add the digits: - Start from the right: $6 + 5 = 11$. Place a $1$ in the tenths column and carry over $1$.
Step 3: Add the whole number part considering any carry: - $0 + 0 + 1$ (from the carry) = $1$.

The sum of $0.6$ and $0.5$ gives $1.1$.

Therefore, the solution to the problem is $1.1$.

To solve this problem, we will add the decimal numbers 0.5 and 0.5 together. The process involves:

• Step 1: Align the decimal points of both numbers, which results in:

0.5
+ 0.5

• Step 2: Start adding from the rightmost digit (tenths position in this case). The digits in the tenths position are both 5. Adding them gives 5 + 5 = 10. Because this is in the tenths position, write 0 in the tenths column, and carry over 1 to the units column.
• Step 3: Proceed to the units column. The digits are 0 in the top row and 0 in the bottom row, while you have a carryover of 1. Therefore, 1 (carry) + 0 + 0 = 1.

Therefore, the sum of 0.5 + 0.5 is precisely $1$.

Given that this was a multiple-choice question, the correct answer is choice 2: 1.

To solve this problem, we will add the two decimal fractions $0.7$ and $0.4$.

Let's break down the process:

• Step 1: Align the numbers by their decimal points:
  $\phantom{+}0.7$
  $+0.4$
• Step 2: Add the numbers column by column starting from the rightmost place (tenths place):
  $7 + 4 = 11$
• Step 3: Write down the 1 in the tenths place and carry over 1 to the units place. There is no whole number component in this addition, so simply add the carry to $0$ which is $1 + 0 = 1$.
• Step 4: Combine the results to find the total: $1.1$.

Thus, the sum of $0.7$ and $0.4$ is $\mathbf{1.1}$.

The correct choice is 1: 1.1.