Multiplying and Dividing Decimal Fractions by 10, 100, etc.: Multiplication by numbers greater than 100

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

• Step 1: Convert the multiplication into a simpler operation by treating decimals appropriately.
• Step 2: Perform the multiplication.
• Step 3: Adjust the result for decimal placement.

Now, let's work through each step:
Step 1: We need to find the result of multiplying $0.15$ by $200$.
Step 2: Multiply as if $0.15$ is $15$, then apply appropriate scaling for the decimal places:
$15 \times 200 = 3000$
Step 3: Since $0.15$ has two decimal places, divide the result by $100$:
$\frac{3000}{100} = 30$

Therefore, the solution to the problem is $30$.

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

• Step 1: Multiply the numbers.
• Step 2: Consider the decimal places.

Let's go through each step:
Step 1: We start by calculating the product of $1.23$ and $180$. Multiplying the numbers without considering the decimal initially, we treat it as $123 \times 180$.
Step 2: Calculate $123 \times 180$. This can be split into simpler calculations, $123 \times (100 + 80)$:
- $123 \times 100 = 12300$
- $123 \times 80 = 9840$
Adding these: $12300 + 9840 = 22140$.
Since $1.23$ has two decimal places, we place the decimal point back in the product, which gives us $221.40$, or simplified, $221.4$.

Therefore, the solution to the problem is $221.4$.

To solve this problem, we need to calculate the product of $0.4$ and $115$.

First, let's perform the multiplication:

Multiply $115$ by $0.4$:

Here's how the calculation works step-by-step:

• Consider $0.4$ as $\frac{4}{10}$.
• Therefore, the multiplication becomes $115 \times \frac{4}{10}$.
• Perform the multiplication first: $115 \times 4 = 460$.
• Then divide by $10$ to manage the decimal place:$\frac{460}{10} = 46$.

Thus, the solution to the problem is $46$.

We will use the distributive property to split 110 into two numbers—100 and 10. 

Now we will multiply the original number (1.23) by these two numbers:

1.23*100=123

1.23*10=12.3

All that is left to do is to add the two products together to get our answer:

123 + 12.3 = 135.3

To solve this problem, we'll proceed with these steps:

• Step 1: Multiply 146 by 150, ignoring the decimal point initially.
• Step 2: Adjust for the decimal point after completing the multiplication.

Step 1: Consider 14.6 as 146, so multiply 146 by 150:

• First, multiply 146 by 10: $146 \times 10 = 1460$.
• Next, multiply 1460 by 15. We can break this into smaller steps:
• $1460 \times 15$ can be computed as $(1460 \times 10) + (1460 \times 5)$.
• $1460 \times 10 = 14600$.
• $1460 \times 5 = 7300$.
• Add these products: $14600 + 7300 = 21900$.

Step 2: Since we treated 14.6 as 146 (multiplied by 10 initially), divide the result by 10:

• $21900 \div 10 = 2190$.

Therefore, the product of $14.6 \times 150$ is $2190$.

To solve this problem, we'll use straightforward multiplication while carefully considering the decimal place. Here are the steps we'll follow:

• Step 1: Treat $0.113$ as $113$ by ignoring the decimal point temporarily.

• Step 2: Multiply $113 \times 170$.

• Step 3: Reintroduce the decimal point in the product by placing it three decimal places from the right, as in $0.113$.

Let's work through each step:

Step 1: We rewrite $0.113$ as $113$.

Step 2: Multiplying $113$ by $170$ yields:

$\begin{aligned} 113 \times 170 &= 113 \times (100 + 70)\\ &= 113 \times 100 + 113 \times 70\\ &= 11300 + 7910\\ &= 19210 \end{aligned}$

Step 3: Now place the decimal point. Since the original number $0.113$ had three decimal places, the product $19210$ must be adjusted to three decimal places from the right, yielding:

$\begin{aligned} 19.210 \end{aligned}$

Thus, the final answer is:

$19.21$

To solve this problem, we'll multiply the decimal number 5.11 by the integer 110. To do this, we'll follow these main steps:

• Step 1: Treat the decimal number 5.11 temporarily as 511 by ignoring the decimal point. This helps us simplify the multiplication process.
• Step 2: Multiply 511 by 110, as if they were whole numbers:

$511 \times 110$

• Step 3: Calculate the product:

$511 \times 110 = 56210$

• Step 4: Since the original problem involved a decimal (two decimal places in number 5.11), adjust the product to account for these two decimal places by dividing by 100:

$56210 \div 100 = 562.1$

Therefore, the solution to the problem is $562.1$.

To solve $3.12 \times 109$, we proceed as follows:

• Step 1: Multiply the numbers as if they were whole numbers. Multiply $312$ by $109$.
• Step 2: Calculate $312 \times 109$:
  • $312 \times 100 = 31200$
  • $312 \times 9 = 2808$
  • Add the two results: $31200 + 2808 = 34008$.
• Step 3: Adjust for decimal places. Since $3.12$ has two decimal places, divide $34008$ by $100$ to get $340.08$.

Therefore, the solution to the multiplication is $340.08$.

To solve this problem, we'll use the distributive property of multiplication:

• Step 1: Decompose $101$ into $100 + 1$.
• Step 2: Apply the distributive property: $11.2 \times (100 + 1) = (11.2 \times 100) + (11.2 \times 1)$.
• Step 3: Calculate $11.2 \times 100$ and $11.2 \times 1$, then add the results.

Now, let's execute each step:
Step 1: Write $101$ as $100 + 1$.
Step 2: Use the distributive property:
$11.2 \times 101 = 11.2 \times (100 + 1) = (11.2 \times 100) + (11.2 \times 1)$.

Step 3: Perform each multiplication:
$11.2 \times 100 = 1120$.
$11.2 \times 1 = 11.2$.

Adding the results: $1120 + 11.2 = 1131.2$.

Thus, the product of $11.2 \times 101$ is $1131.2$, which matches the correct choice from the provided list.