Addition and Subtraction of Decimal Fractions: Identify whether the exercise is 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.

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

Therefore, the exercise is not written correctly.

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.

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.

The problem requires us to verify if the subtraction exercise of the decimal numbers is written correctly, focusing on the position of the decimal points.

Step-by-step:

• Step 1: Identify the given numbers, $2.10$ and $3.2$.

• Step 2: Align these numbers by their decimal points for proper subtraction.

Upon alignment, the numbers are:

$2.10$
$-3.2$.

To correctly align them for subtraction, we can rewrite $3.2$ as $3.20$ to match the number of decimal places:

$2.10$

$-3.20$

The decimal points are aligned correctly in both numbers, confirming that the exercise is set up accurately regarding the position of the decimal point.

Thus, the answer to the problem is Yes.

To determine if the exercise is correctly written, let's ensure the decimal points are aligned properly in the subtraction problem. We have:

• Top number: $88.100$
• Bottom number: $88.101$

We verify that each digit is aligned according to its place value:

• The units column aligns ($8$ above $8$).
• The tenths, hundredths, and thousandths columns align ($0$ above $1$).
• The decimal points are directly above one another.

Since the digits and decimal points are aligned properly according to the rules of subtracting decimal numbers, we can conclude that the setup of the exercise is correct. Therefore, the assertion that "the position of the decimal point corresponds" is True.

In conclusion, the exercise is correctly written regarding the alignment of the decimal point.

To effectively assess the problem, we should confirm if the decimal points in the subtraction of two identical numbers, $99.38 - 99.38$, are aligned correctly.

Step 1: The numbers involved in the subtraction are $99.38$ and $99.38$, both having the same number of digits before and after the decimal point.

Step 2: Check the alignment of the decimal points in the subtraction setup. In properly written subtraction involving decimals, the decimal points must align vertically to ensure correct digit placement.

Step 3: The setup displays the numbers:

• $99.38$
• $99.38$

Each digit before and after the decimal is in perfect vertical alignment, confirming correct decimal point alignment.

Conclusion: The exercise is correctly written in terms of decimal alignment.

The correct answer to the problem is True.

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

• Ensure the decimal numbers are aligned correctly according to their decimal points.

• Perform the arithmetic operation to verify logical correctness.

Let's analyze the given numbers:

• The first number is $38.15$.

• The second number is $122.3$. We can express this as $122.30$ to simplify alignment.

Align the numbers vertically based on their decimal points:

$\quad 38.15$
$-122.30$

Notice the decimal points are aligned. Now, perform the subtraction:

Start from the rightmost column:

• $(5 - 0 = 5)$

• $(1 - 3 = \text{Borrow } 10, \text{ becomes } 11 - 3 = 8)$

Move to the next left column (tens column):

• $(\text{borrowed } 1 \rightarrow 8 \text{ becomes } 7)$

• $(7 - 2 = 5)$

• $(3 - 2 = 1)$

• $(\text{The result is negative because 38.15 is less than 122.30})$

Result of the subtraction is $-84.15$.

Since the exercise primarily asks if the decimal points are aligned correctly, and they indeed align correctly, we conclude:

The exercise is written correctly with respect to decimal alignment.

Therefore, the solution to the problem is True.

To determine whether the exercise is set correctly, we need to align the decimal points of the two numbers involved in the subtraction operation:

1. The given numbers are 38.15 and 122.3.
2. We write them down vertically, aligning by the decimal points:

$\begin{array}{c} \hphantom{0}38.15 \\ - \hphantom{0}122.3 \\ \end{array}$

3. Notice that the number 38.15 has two decimal places (hundredths), while 122.3 only has one decimal place (tenths). Therefore, the hundredths place in 122.3 is effectively considered as "0" to match the decimal places of the first number. Upon aligning the decimal points, 38.15 and 122.3 indeed match as:

$\begin{array}{c} \hphantom{0}38.15 \\ - 122.30 \\ \end{array}$

4. This check confirms that there is an incorrect statement regarding "The position of the decimal point corresponds," as the numbers are aligned at the decimal points considering all decimal places are consistently represented.

Therefore, the statement "The position of the decimal point corresponds" is Not true.

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

• Step 1: Align the decimal numbers by their decimal points.
• Step 2: Check if each digit is correctly aligned with its corresponding digit based on place value.
• Step 3: Ensure the operation symbol is properly placed.

Now, let's work through each step:
Step 1: Start with the number 13.45 and align 3.21 directly below it such that the decimal points are vertically aligned. This ensures that the tenths, hundredths, and whole numbers are in the correct columns.
Step 2: Verify that: - The '1' in 13.45 is in the tens place, and the '3' in 3.21 is in the ones place, both aligned left of the decimal. - The '3' in 13.45 and '2' in 3.21 are aligned in the tenths column. - The '4' in 13.45 and '1' in 3.21 are in the hundredths column.
Step 3: Place the '+' sign outside and to the left, in line with the numbers, ensuring it is clearly indicating addition.

Therefore, the correct alignment for the addition of these decimal numbers is:

To correctly set up a vertical addition of decimal fractions, it is crucial to align the numbers by their decimal points. Let's break down the choices:

• Choice 1 presents the numbers in the proper format. The decimal points of $15.5604$ and $4.32$ align vertically, ensuring accurate addition.

• Choice 2 misaligns the decimal points, incorrectly starting $4.32$ further to the left than necessary.

• Choice 3 also misaligns the decimals, wanting to begin $4.32$ even further than choice 2.

Thus, the correct choice is Choice 1, since it correctly aligns the numbers by their decimal points, facilitating accurate addition of the values involved.

Therefore, the correct format choice is Choice 1.

To solve this problem, we need to verify if the numbers are properly aligned for subtraction:

• Step 1: Identify the given numbers. We have the numbers 16.234 and 5.35 written in a vertical format.
• Step 2: Check if decimal points are aligned. For proper subtraction of decimal numbers, the decimal points in both numbers should line up vertically.
• Step 3: Align digits relative to their place values. We need to compare the positioning of digits before and after the decimal point to confirm correct alignment.

Now, let's apply these steps:
Step 1: We have the numbers $16.234$ and $5.35$.
Step 2: Inspect the vertical alignment of the decimal points. We notice that $16.234$ has three digits after the decimal, while $5.35$ has only two digits.
Step 3: Evaluate the alignment. The decimal point in $5.35$ is not properly aligned because it does not have the same number of decimal places as $16.234$.

Therefore, the format is not correct for vertical subtraction, as the alignment of decimal points and digits is incorrect. Hence, the correct answer is No.

When setting up a subtraction problem with decimals, it is crucial that the decimal points in both numbers directly align. This ensures that each digit is correctly placed in its respective place value column (units, tenths, hundredths, etc.) to facilitate accurate subtraction.

In this problem, the number $25.754$ is aligned vertically with $3.13$. Upon inspection, both decimals are indeed arranged vertically so that the decimal points are in the same column. The digits following the decimal in $3.13$ are tenths and hundredths, leaving the thousandths position empty, which is acceptable as we can treat the missing place value as zero for alignment purposes (i.e., treat $3.13$ as $3.130$).

Therefore, the numbers are set up correctly for vertical subtraction, where:

This alignment confirms that the subtraction operation can reliably proceed as the format is correct.

Therefore, the correct answer to the problem is Yes.

To determine if the addition of decimals is set up correctly, follow these steps:

• Step 1: Check the alignment of the decimal points in both numbers.
• Step 2: Ensure each corresponding place value (units, tenths, hundredths, etc.) is aligned vertically.
• Step 3: Look at the layout provided:
  $\begin{array}{c} 7.462 \\ +\phantom{.}2.13 \\ \hline \end{array}$

The first number, $7.462$, has three decimal places, whereas the second number, $2.13$, has two decimal places. The decimal point in $2.13$ should be directly below the decimal point in $7.462$. However, it appears that the digits in the tenths and hundredths place of $2.13$ are not properly aligned with $7.462$. Hence, the addition is not aligned correctly as the decimal points are not vertically aligned.

Therefore, the addition layout is incorrect, and the solution to the problem is:

No