Multiplication of Decimal Fractions: Solving an exercise

To solve this problem, we'll proceed with the multiplication of the decimals $5.7$ and $2.9$.

• Step 1: Eliminate the decimal points by treating the numbers as whole numbers. Transform $5.7$ to $57$ and $2.9$ to $29$.
• Step 2: Multiply the whole numbers $57 \times 29$. We can perform the multiplication as follows:
  • Multiply: $57 \times 9 = 513$
  • Multiply: $57 \times 2 = 114$, adjust for place value: $1140$
  • Add these results: $513 + 1140 = 1653$
• Step 3: Adjust for the decimal point. Since we transformed $5.7$ and $2.9$ by moving the decimal one place each (total of two places), we need to return two decimal places in the product $1653$.
• Result after adjusting the decimal point: $16.53$

Therefore, the value of $x$ is $\bold{16.53}$.

This matches choice 4 from the provided multiple-choice options.

Therefore, the final answer is $\bold{16.53}$.

The problem is to find the value of $x$ when multiplying 8.5 by 1.5. To solve this:

• Step 1: Write the numbers 8.5 and 1.5 without the decimal points: 85 and 15.
• Step 2: Multiply these whole numbers: $85 \times 15 = 1275$
• Step 3: Count the total number of decimal places in both original numbers. 8.5 has one decimal place, and 1.5 has one decimal place, giving a total of two decimal places.
• Step 4: Place the decimal point in your product so that there are two digits to the right of the decimal: $12.75$

Hence, the value of $x$ is $12.75$.

To solve the multiplication problem of decimals 2.15 and 1.23, we adhere to the following steps:

• Step 1: Consider the numbers as integers, 215 and 123.

• Step 2: Perform the multiplication: $215 \times 123$.

• Step 3: The number of decimal places in the factors is 2 and 2, thus 4 decimal places are needed in total in the final result.

Let's proceed with the calculation:

$215 \times 123$ involves standard multiplication:

   215
×  123
------
   645   (215 × 3)
  430    (215 × 2, shifted one place)
+215     (215 × 1, shifted two places)
------
  26445

This calculation results in 26445. To correctly place the decimal point, note that 2.15 has 2 decimal places, and 1.23 has 2 decimal places, so we need a result with 4 total decimal places.

Therefore, position the decimal point four places from the right in our product, giving $2.6445$.

Thus, the product of 2.15 and 1.23 is $2.6445$.

To solve this problem, we'll follow the steps of multiplying decimals:

• Step 1: Write the numbers involved as $x = 3.88$ and $y = 2.26$.
• Step 2: Convert these numbers into their integer equivalents by removing the decimal points.
• Step 3: Multiply the integer forms of these numbers.
• Step 4: Place the decimal point in the result based on the total number of decimal places from the original numbers.

Let's go through these steps:

Step 1: Our numbers are $3.88$ and $2.26$.
Step 2: Turn these into integers. To do this, observe that there are a total of 4 decimal places (2 in each number):

• $3.88 \times 100 = 388$
• $2.26 \times 100 = 226$

Step 3: Multiply the integers: $388 \times 226$.

This multiplication yields: $388 \times 226 = 87688$

Step 4: We need to adjust by placing the decimal point in the appropriate position. Since the original numbers had a total of 4 decimal places, the product should likewise have 4 decimal places:
Insert the decimal: $87688 \rightarrow 8.7688$

Therefore, the product of $3.88$ and $2.26$ is $8.7688$.

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

• Step 1: Multiply the numbers as if they were whole numbers: $237 \times 12$.
• Step 2: Count the decimal places in each number: $2$ places in $2.37$ and $2$ places in $0.12$, totaling $4$ decimal places.
• Step 3: Place the decimal point in the result from step 1 to reflect these $4$ decimal places.

Now, let's work through each step:

Step 1: Multiply the whole numbers $237 \times 12 = 2844$.

Step 2: The total decimal places in the original numbers is $4$.

Step 3: Place the decimal point to give us $0.2844$, since we need $4$ decimal places.

Therefore, the solution to the problem is $0.2844$.

Let's solve the problem through these detailed steps:

Step 1: Multiply the numbers without considering the decimal points:
We multiply $145$ (from $1.45$) by $327$ (from $3.27$).

Step 2: Perform the multiplication:
$145 \times 327$

Calculate:

$\begin{aligned} &145 \times 7 = 1015, \\ &145 \times 20 = 2900, \\ &145 \times 300 = 43500. \end{aligned}$
The sum of these partial products:
$1015 + 2900 + 43500 = 47415.$

Step 3: Consider the decimal points:
The number $1.45$ has 2 decimal places, and $3.27$ also has 2 decimal places, for a total of 4 decimal places.
Place the decimal point 4 places from the right in the product $47415$.

The resulting product is $4.7415$.

Therefore, the solution to the problem is $4.7415$.

To solve this problem, we'll multiply two decimal numbers, $2.4$ and $31.61$. To ensure accuracy, we'll follow these steps:

• Step 1: Treat the numbers as whole numbers by removing the decimal points: $24$ and $3161$.
• Step 2: Multiply these numbers: $24 \times 3161 = 75864$.
• Step 3: Count the total number of decimal places in the original factors. Here, $2.4$ has one decimal place, and $31.61$ has two, for a total of three decimal places.
• Step 4: Place the decimal point in the product so it has three decimal places: $75.864$.

Therefore, the product of $2.4$ and $31.61$ is $75.864$.

The correct choice from the possible answers is $75.864$.

To find the value of $x$, we will multiply the two decimal numbers given:

• The numbers to be multiplied are $2.82$ and $3.1$.
• First, ignore the decimal places and multiply the numbers as if they were whole: $282 \times 31$.
• Calculate $282 \times 31$:
  $282 \times 31 = 282 \times (30 + 1) = (282 \times 30) + (282 \times 1)$.
• Calculating these values individually:
  $282 \times 30 = 8460$ (shift $282$ to the left by one decimal place)
  $282 \times 1 = 282$.
• Adding these results gives $8460 + 282 = 8742$.
• Determine the correct placement of the decimal point:
  - $2.82$ has 2 decimal places, and $3.1$ has 1 decimal place,
  - In total, there are $2 + 1 = 3$ decimal places.
• Place the decimal point in $8742$ so that it has three decimal places from the right: $8.742$.

Therefore, the value of $x$ is $x = 8.742$.

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

• Step 1: Ignoring the decimal points, multiply 824 by 55 as if they were whole numbers.
• Step 2: Calculate the product of these whole numbers.
• Step 3: Adjust the product to account for the original decimal places.

Now, let's work through each step:
Step 1: Ignoring the decimal points, we will multiply 824 and 55.
Step 2: Perform the multiplication:

• $824 \times 55 = (824 \times 50) + (824 \times 5)$
• $824 \times 50 = 41200$
• $824 \times 5 = 4120$
• Add these two products: $41200 + 4120 = 45320$

Step 3: Consider the decimal places. There are a total of 3 decimal places: 2 in 8.24 and 1 in 5.5.
Therefore, the final product should have 3 decimal places.

Adjust the product: Starting with 45320, place the decimal to yield $\underline{\mathbf{45.320}}$.

Therefore, the value of $x$ is $45.320$.

To solve this problem, we'll multiply two decimal numbers: $17.331$ and $2.55$. Follow these steps:

• Step 1: Ignore the decimal points initially and perform multiplication: $17331 \times 255$.

• Step 2: Multiply the numbers as if they were whole numbers: $\begin{aligned} 17331 \times 255 = 4419405 \end{aligned}$

• Step 3: Count the total number of decimal places in the original numbers:

  • $17.331$ has 3 decimal places.

  • $2.55$ has 2 decimal places.

  • Total decimal places = 3 + 2 = 5.

• Step 4: Place the decimal in the product. Starting from the right, place the decimal point 5 positions to the left in the number $4419405$.

• This gives $\begin{aligned} 44.19405 \end{aligned}$.

Therefore, the product of $17.331$ and $2.55$ is $44.19405$.