Dividing Decimal Fractions: Solving the problem

To solve the division problem $2.6 \div 0.1$, we can simplify the division by eliminating the decimal in the divisor:

• Multiply both the dividend $2.6$ and the divisor $0.1$ by 10 to get rid of the decimal in the divisor. This gives $2.6 \times 10 = 26$ and $0.1 \times 10 = 1$.
• Now, the division simplifies to $26 \div 1$.
• Dividing $26$ by $1$ gives us $26$.

Thus, the solution to the division problem $2.6 \div 0.1$ is $26$.

To solve the problem $0.1 \div 0.02$, let's follow these steps:

• Step 1: Eliminate the decimals by multiplying both the dividend and divisor by 100 to convert them to whole numbers.
• Step 2: Convert $0.1$ to $10$ and $0.02$ to $2$ by multiplication.
• Step 3: Perform the division $10 \div 2$.

Now, let's proceed with the calculations:
- When we multiply $0.1$ by 100, we get $10$. Similarly, multiplying $0.02$ by 100 gives us $2$.
- Next, we divide $10$ by $2$:
$10 \div 2 = 5$.

Therefore, the solution to the problem is $5$.

To solve the problem $0.4 \div 0.2$, we can follow these steps:

• Step 1: Convert the division of decimals into a division of whole numbers by multiplying both the dividend (0.4) and the divisor (0.2) by 10.
• Step 2: This operation results in dividing 4 by 2 (since $0.4 \times 10 = 4$ and $0.2 \times 10 = 2$).
• Step 3: Perform the division $4 \div 2$, which equals 2.

Thus, the result of dividing $0.4$ by $0.2$ is $\boxed{2}$.

To solve the problem of dividing $1.1$ by $0.5$, let's simplify the operation by converting the decimals into whole numbers:

• Step 1: Multiply both the dividend and the divisor by $10$ to eliminate the decimal points:
  $1.1 \times 10 = 11$
  $0.5 \times 10 = 5$

• Step 2: Perform division on the whole numbers:
  $11 \div 5 = 2.2$

• Step 3: Interpret the result. We found that the answer to the division $1.1 \div 0.5 = 2.2$.

Therefore, the solution to the problem is $2.2$.

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

• Step 1: Convert each decimal to a fraction.
• Step 2: Divide by converting to multiplication using reciprocals.
• Step 3: Simplify the resulting fraction to find the solution.

Now, let's proceed with the calculations:

Step 1: Convert $1.3$ and $0.2$ to fractions:

• $1.3 = \frac{13}{10}$
• $0.2 = \frac{2}{10}$

Step 2: Perform division by multiplying by the reciprocal:

$\frac{13}{10} \div \frac{2}{10} = \frac{13}{10} \times \frac{10}{2}$

Step 3: Simplify the fractions:

• Cancel the common factor of 10: $\frac{13 \times 10}{10 \times 2} = \frac{13}{2}$
• Calculate the division: $\frac{13}{2} = 6.5$

Therefore, the solution to the problem is $6.5$.

To solve the division of two decimal numbers $0.49$ and $0.7$, we will follow these steps:

• Step 1: Convert the decimals to fractions. Since $0.49$ has two decimal places, it can be written as $\frac{49}{100}$. Similarly, $0.7$, which has one decimal place, can be written as $\frac{7}{10}$.
• Step 2: Set up the division of fractions: $\frac{49}{100} \div \frac{7}{10}$.
• Step 3: Recall that division by a fraction is the same as multiplication by its reciprocal. Thus, we rewrite the division as multiplication by the reciprocal of $\frac{7}{10}$:

$\frac{49}{100} \times \frac{10}{7}$.

• Step 4: Multiply the numerators and the denominators:

$\frac{49 \times 10}{100 \times 7} = \frac{490}{700}$.

• Step 5: Simplify the fraction by finding the greatest common divisor (GCD) of $490$ and $700$. The GCD is $70$.

After dividing both the numerator and the denominator by $70$, we have:

$\frac{490 \div 70}{700 \div 70} = \frac{7}{10}$.

Thus, the result of $0.49 \div 0.7$ is $\frac{7}{10}$, which is $0.7$.

Therefore, the solution to the problem is $0.7$.

To solve this problem of dividing $1.1$ by $0.2$, we can follow these steps:

• Step 1: Remove the decimals by multiplying both numbers by 10. This makes the division simpler with whole numbers.
• Step 2: Multiply $1.1$ by 10 to get $11$, and multiply $0.2$ by 10 to get $2$.
• Step 3: Now perform the division $11 \div 2$.

Let's perform the calculation:

• Step 1: The division $11 \div 2$ is performed as follows:
• Step 2: By dividing $11$ by $2$, we note that $2$ goes into $11$ exactly $5$ times to give $10$, with a remainder of $1$.
• Step 3: Continue by considering the remainder as a decimal: $1.0 \div 2 = 0.5$ (as $2$ goes into $10$ exactly $5$ times).
• Step 4: Adding the whole and decimal parts together gives us $5 + 0.5 = 5.5$.

Therefore, the solution to the problem $1.1 \div 0.2$ is $5.5$.

To solve the division of decimals $0.5 \div 0.2$, follow these tried and true steps:

• **Step 1:** Multiply both the dividend $0.5$ and the divisor $0.2$ by 10 to remove the decimal points. This transforms the problem into an equivalent with whole numbers: $5 \div 2$.

• **Step 2:** Perform the division of the resulting whole numbers: $5 \div 2 = 2.5$.

• **Step 3:** Thus, the answer to the original division problem $0.5 \div 0.2$ is $2.5$.

Therefore, the solution to the problem is $2.5$.

To solve the problem $1.6 \div 0.2$, we will eliminate the decimals by converting the numbers into whole numbers and performing the division.

• Step 1: Convert the decimals to whole numbers. Multiply both 1.6 and 0.2 by 10 to remove the decimal places.
  $1.6 \times 10 = 16$ and $0.2 \times 10 = 2$.
• Step 2: Perform integer division. Now divide the two whole numbers obtained:
  $16 \div 2 = 8$.
• Step 3: Verify the result. Verify by direct division using decimals:
  Perform $1.6 \div 0.2$ which is equivalent to $\frac{16}{2} = 8$.

The calculation confirms that our approach is correct, ensuring accuracy both in removing decimals and dividing.

Therefore, the solution to $1.6 \div 0.2$ is $8$.

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

• Step 1: Convert $0.3$ (the divisor) into a whole number by multiplying both $0.18$ and $0.3$ by 10.
• Step 2: Perform the division with whole numbers.

Let's perform the steps:

Step 1: Multiply both $0.18$ and $0.3$ by 10 to get:

$(0.18 \times 10) = 1.8$

$(0.3 \times 10) = 3$

Step 2: Now divide the whole numbers:

$\frac{1.8}{3} = 0.6$

Thus, the division of $0.18$ by $0.3$ results in $0.6$.

To solve the problem of dividing $0.64$ by $0.8$, we need to convert the decimals to whole numbers to simplify the process. Here's a step-by-step solution:

• Step 1: Notice both numbers are decimals. Our goal is to make them whole numbers to simplify the division.
• Step 2: The number $0.64$ can be written as $\frac{64}{100}$ and $0.8$ as $\frac{8}{10}$. To eliminate decimals, multiply both numbers by 100 (the larger factor of 10 to ensure both numbers become integers): $0.64 \times 100 = 64$ and $0.8 \times 100 = 80$.
• Step 3: Perform the division using these whole numbers: $\frac{64}{80}$.
• Step 4: Simplify $\frac{64}{80}$. The greatest common divisor of 64 and 80 is 16. Thus, dividing both the numerator and the denominator by 16, we get $\frac{64 \div 16}{80 \div 16} = \frac{4}{5}$.
• Step 5: Convert $\frac{4}{5}$ to decimal form. To do this, divide 4 by 5, which gives us $0.8$.

Therefore, the solution to the problem $0.64 \div 0.8$ is $0.8$.

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

• Step 1: Eliminate decimals by multiplying both numbers by 10.
• Step 2: Perform integer division.
• Step 3: Evaluate and verify the final answer.

Now, let's work through each step:
Step 1: Multiply both numbers $2.4$ and $1.2$ by 10 to eliminate the decimal points. This gives us $24$ and $12$, respectively.
Step 2: Divide the integers: $24 \div 12 = 2$.
Step 3: Verify: Multiplying the result $2$ by $1.2$ should give us $2.4$, confirming the division is correct.

Therefore, the solution to the problem is $\boxed{2}$.

To solve the division problem $0.36 \div 0.06$, we'll follow these steps:

• Step 1: Eliminate the decimals:

Both $0.36$ and $0.06$ are decimal numbers. In order to make the division easier, multiply both numbers by 100 to remove the decimals:

• $0.36 \times 100 = 36$
• $0.06 \times 100 = 6$

Converting the problem, we now have $36 \div 6$.

• Step 2: Perform the division:

Now divide $36$ by $6$:

$36 \div 6 = 6$

Therefore, the solution to the problem $0.36 \div 0.06$ is $6$.

To solve the problem of dividing 1.49 by 0.2, we will first remove the decimals by multiplying both the dividend and the divisor by the same power of ten, allowing us to work with whole numbers. This will make division easier and more straightforward.

Steps to solve the problem:

• Step 1: Identify the decimal point in the divisor, which is 0.2. It has 1 decimal place.
• Step 2: To eliminate the decimal, multiply both the divisor (0.2) and the dividend (1.49) by 10 (since the divisor has 1 decimal place).
• Step 3: Performing the multiplication, we have:
  Dividend: $1.49 \times 10 = 14.9$
  Divisor: $0.2 \times 10 = 2$
• Step 4: Now, divide the result from Step 3 using whole numbers:
  $14.9 \div 2 = 7.45$

Therefore, the solution to the problem is $7.45$.

To solve this problem, we will follow these steps:

• Step 1: Remove the decimals by multiplying both the dividend and the divisor by the same power of 10.
• Step 2: Perform the division on the resulting whole numbers.
• Step 3: Simplify and verify the result against the multiple-choice options.

Now, let's work through the solution:

Step 1: Multiply both 15.5 and 0.5 by 10 to eliminate the decimals.
$15.5 \times 10 = 155$
$0.5 \times 10 = 5$

Step 2: Divide the resulting whole numbers:
$155 \div 5 = 31$

Step 3: We check the result against the choices. The result $31$ corresponds to choice 1.

Therefore, the solution to the problem is $31$.

To solve the problem $4.4 \div 1.1$, we will proceed with the following steps:

• Step 1: Convert the decimals to whole numbers. Multiply both the numerator (4.4) and the denominator (1.1) by 10 to eliminate the decimal points, resulting in $44 \div 11$.
• Step 2: Perform the division $44 \div 11$. Since $44$ divided by $11$ is $4$, the quotient is 4.
• Step 3: Interpret and verify the result. Since multiplying by 10 does not affect the ratio (or quotient), the result is valid for the original problem.

Therefore, the solution to the problem $4.4 \div 1.1$ is $4$.

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

• Step 1: Convert the problem to integer division.
• Step 2: Perform the division.
• Step 3: Adjust for decimal placement.

Now, let's work through each step:

Step 1: Convert the problem to integer division.
Multiply both 10.9 and 2.5 by 10 to eliminate the decimals, yielding 109 and 25, respectively.

Step 2: Perform the division.
Divide 109 by 25. When dividing, you get 4 as the quotient and a remainder of 9. Therefore, 109 ÷ 25 = 4.36.

Step 3: Adjust for decimal placement.
Since we initially multiplied by 10, dividing by 25 effectively places the decimal in the correct position. Thus, 10.9 ÷ 2.5 = 4.36.

Therefore, the solution to the problem is $4.36$.

To solve this problem, we need to divide $10.4$ by $5.2$. We can achieve this by simplifying the division process:

• Step 1: Eliminate decimals by multiplying both numbers by 10. Thus, we have $10.4 \times 10 = 104$ and $5.2 \times 10 = 52$.
• Step 2: Now, divide the resulting integers: $\frac{104}{52}$.
• Step 3: Perform the division: $104 \div 52 = 2$.

Thus, the result of dividing $10.4$ by $5.2$ is $\mathbf{2}$.

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

• Step 1: Eliminate decimals by multiplying both the dividend and the divisor by $10$.
• Step 2: Perform the division on the whole numbers obtained.
• Step 3: Interpret the result based on the transformation performed.

Now, let's work through each step:
Step 1: Multiply $6.36$ and $0.6$ by $10$. This gives:

$6.36 \times 10 = 63.6$ and $0.6 \times 10 = 6$.

Step 2: Perform the division $63.6 \div 6$:
Divide $63.6$ by $6$, which is equivalent to $63.6 \div 6 = 10.6$.

Therefore, the solution to the problem is $10.6$.

To solve the division of decimals problem $14.7 \div 0.07$, we'll follow these steps:

• Step 1: Eliminate the decimals by converting to whole numbers.
• Step 2: Perform the division with the resulting whole numbers.
• Step 3: Evaluate the result.

Let's break these steps down:

Step 1: To make the numbers whole, multiply both 14.7 and 0.07 by 100. This shifts the decimal point two places to the right in each number.
$14.7 \times 100 = 1470 \quad \text{and} \quad 0.07 \times 100 = 7$

Step 2: Now, divide the resulting whole numbers:
$1470 \div 7$

Step 3: Perform the division:
$1470 \div 7 = 210$

Therefore, the calculated result of $14.7 \div 0.07$ is $210$, matching the correct answer choice.