Decimal Fractions Practice Problems - Advanced Math

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:

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 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.