Subtraction of Fractions: One of the denominators is the common denominator

To solve the problem $\frac{1}{4} - \frac{1}{8}$, we need to subtract these two fractions:

Step 1: Determine the common denominator.
The denominators are 4 and 8. The least common multiple of 4 and 8 is 8.

Step 2: Convert each fraction to an equivalent fraction with the common denominator of 8.
- Convert $\frac{1}{4}$ to $\frac{1 \times 2}{4 \times 2} = \frac{2}{8}$
- The fraction $\frac{1}{8}$ already has the denominator 8.

Step 3: Subtract the numerators.
Subtract $\frac{1}{8}$ from $\frac{2}{8}$:
$\frac{2}{8} - \frac{1}{8} = \frac{2 - 1}{8} = \frac{1}{8}$

The resulting fraction is already in its simplest form.

Therefore, the solution to the problem is $\frac{1}{8}$.

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

• Step 1: Convert $\frac{1}{2}$ to a fraction with denominator $10$.
• Step 2: Subtract $\frac{2}{10}$ from the converted fraction.
• Step 3: Simplify the result, if necessary.

Let's go through each step:

Step 1: Convert $\frac{1}{2}$ into a fraction with a denominator of $10$.
We know that $\frac{1}{2}$ is equivalent to multiplying the numerator and the denominator by $5$:
$\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$

Step 2: Subtract $\frac{2}{10}$ from $\frac{5}{10}$.
Subtract by keeping the denominator $10$ and subtract the numerators:
$\frac{5}{10} - \frac{2}{10} = \frac{5-2}{10} = \frac{3}{10}$

Step 3: Simplify the result.
The fraction $\frac{3}{10}$ is already in its simplest form.

Therefore, the solution to the problem is $\frac{3}{10}$.

To solve $\frac{3}{5} - \frac{6}{15}$, we need both fractions to have the same denominator. We observe that 15 is a multiple of 5, so it is already suitable as a common denominator.

Step 1: Convert
Convert $\frac{3}{5}$ to have a denominator of 15. Multiply both the numerator and the denominator by 3:

$\frac{3}{5} \times \frac{3}{3} = \frac{9}{15}$

Step 2: Subtract the fractions
Now, subtract $\frac{9}{15} - \frac{6}{15}$:

$\frac{9}{15} - \frac{6}{15} = \frac{9 - 6}{15} = \frac{3}{15}$

Step 3: Simplify the result
Simplify $\frac{3}{15}$ by dividing both the numerator and the denominator by 3:

$\frac{3}{15} = \frac{1}{5}$

Therefore, the solution to the problem is $\frac{1}{5}$.

To solve the problem of subtracting $\frac{1}{9}$ from $\frac{2}{3}$, we need a common denominator. Let's follow these steps:

• Step 1: Identify the common denominator for the fractions $\frac{2}{3}$ and $\frac{1}{9}$. Since $9$ is a multiple of $3$, we use $9$ as the common denominator.
• Step 2: Convert $\frac{2}{3}$ to a fraction with denominator $9$:
  To do this, multiply the numerator and the denominator of $\frac{2}{3}$ by $3$ (since $9$ divided by $3$ is $3$):
  $\frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}$.
• Step 3: Subtract $\frac{1}{9}$ from $\frac{6}{9}$:
  $\frac{6}{9} - \frac{1}{9} = \frac{6 - 1}{9} = \frac{5}{9}$.

Thus, the difference between $\frac{2}{3}$ and $\frac{1}{9}$ is $\frac{5}{9}$.

Therefore, the correct choice from the given options is $\boxed{\frac{5}{9}}$.

To solve the subtraction $\frac{5}{6} - \frac{7}{12}$, we need a common denominator.

Step 1: Find the least common denominator (LCD) of the two fractions.
The denominators are 6 and 12. The least common multiple of 6 and 12 is 12.

Step 2: Convert $\frac{5}{6}$ to an equivalent fraction with a denominator of 12.
We can multiply the numerator and the denominator by 2 to achieve this:
$\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}$.

Step 3: Now, subtract the fractions with a common denominator:
$\frac{10}{12} - \frac{7}{12} = \frac{10 - 7}{12} = \frac{3}{12}$.

Step 4: Simplify the result.
$\frac{3}{12}$ can be simplified by dividing both the numerator and the denominator by 3:
$\frac{3}{12} = \frac{3 \div 3}{12 \div 3} = \frac{1}{4}$.

Therefore, the solution to the problem $\frac{5}{6} - \frac{7}{12}$ is $\boxed{\frac{1}{4}}$.

From the available choices, option 4, which is $\frac{1}{4}$, is the correct answer.

To solve the problem $\frac{3}{4} - \frac{5}{12}$, we need to subtract two fractions with different denominators. Let's follow these steps:

• Step 1: Identify the least common denominator (LCD) of the two fractions. Here, the denominators are 4 and 12. The least common multiple of 4 and 12 is 12.
• Step 2: Convert $\frac{3}{4}$ to an equivalent fraction with a denominator of 12. To do this, we multiply both the numerator and the denominator by 3:
  $\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$
• Step 3: Now that both fractions have the same denominator, we can subtract the numerators:
  $\frac{9}{12} - \frac{5}{12} = \frac{9 - 5}{12} = \frac{4}{12}$
• Step 4: Simplify the fraction $\frac{4}{12}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
  $\frac{4}{12} = \frac{4 \div 4}{12 \div 4} = \frac{1}{3}$

Therefore, the solution to the problem is $\frac{1}{3}$.

To solve this problem, we'll perform the following steps:

• Step 1: Find the Least Common Denominator (LCD) between $4$ and $8$.
• Step 2: Convert both fractions to have this common denominator.
• Step 3: Subtract the numerators, keeping the denominator the same.

Let's apply these steps starting with the first one.

Step 1: Find the Least Common Denominator
The denominators are $4$ and $8$. The least common denominator is the smallest number that both denominators divide into evenly. In this case, the LCD is $8$ because it is the smallest number that is a multiple of both $4$ and $8$.

Step 2: Convert fractions to have the same denominator of $8$
- The fraction $\frac{5}{4}$ needs to be converted to a denominator of $8$. To do this, multiply both the numerator and denominator by $2$:

$\frac{5}{4} \times \frac{2}{2} = \frac{10}{8}$

- The fraction $\frac{3}{8}$ already has the denominator $8$, so it remains unchanged as $\frac{3}{8}$.

Step 3: Subtract the numerators
Now that the fractions have the same denominator, subtract the numerators:

$\frac{10}{8} - \frac{3}{8} = \frac{10 - 3}{8} = \frac{7}{8}$

Therefore, the solution to $\frac{5}{4} - \frac{3}{8}$ is $\frac{7}{8}$.

To solve the problem $\frac{2}{3} - \frac{1}{6}$, we follow these steps:

• Step 1: Identify a common denominator for both fractions. Since 6 is a multiple of 3, we use 6 as the common denominator.
• Step 2: Convert $\frac{2}{3}$ to a fraction with a denominator of 6. To do this, multiply both the numerator and the denominator by 2, giving $\frac{4}{6}$.
• Step 3: The fraction $\frac{1}{6}$ already has the desired denominator, so it remains $\frac{1}{6}$.
• Step 4: Perform the subtraction: $\frac{4}{6} - \frac{1}{6} = \frac{3}{6}$.
• Step 5: Simplify the resulting fraction. Simplify $\frac{3}{6}$ by dividing both numerator and denominator by their greatest common divisor, which is 3, resulting in $\frac{1}{2}$.

Therefore, the solution to the problem is $\frac{1}{2}$.

To solve this problem, we'll follow a step-by-step approach:

• Step 1: Convert both fractions to have the same denominator.
  - The original fractions are $\frac{3}{5}$ and $\frac{5}{10}$.
  - Convert $\frac{3}{5}$ to a fraction with denominator 10. Multiply both numerator and denominator by 2:
  $\frac{3}{5} \times \frac{2}{2} = \frac{6}{10}$.

• Step 2: Subtract the fractions now that they have a common denominator.
  - The fractions to subtract are $\frac{6}{10} - \frac{5}{10}$.

• Step 3: Perform the subtraction by subtracting numerators.
  - $\frac{6}{10} - \frac{5}{10} = \frac{6-5}{10} = \frac{1}{10}$.

• Step 4: Verify if simplification is necessary.
  - The fraction $\frac{1}{10}$ is already in its simplest form.

Therefore, the solution to $\frac{3}{5}-\frac{5}{10}$ is $\frac{1}{10}$.

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

• Step 1: Convert $\frac{3}{4}$ into an equivalent fraction with a denominator of 8.
• Step 2: Subtract the numerators of the equivalent fractions.
• Step 3: Simplify if necessary.

Now, let's work through each step:

Step 1: Find a common denominator for the fractions $\frac{3}{4}$ and $\frac{3}{8}$. The least common denominator is 8.

Convert $\frac{3}{4}$ to an equivalent fraction with a denominator of 8:

$\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$

Step 2: Subtract $\frac{3}{8}$ from $\frac{6}{8}$:

$\frac{6}{8} - \frac{3}{8} = \frac{6 - 3}{8} = \frac{3}{8}$

Step 3: There is no need to simplify further as the fraction $\frac{3}{8}$ is already in its simplest form.

Therefore, the solution to the problem is $\frac{3}{8}$.

To solve this fraction subtraction problem, we need to follow these steps:

• Step 1: Identify and adjust the fractions to have a common denominator. The given problem is $\frac{1}{3} - \frac{1}{6}$.
• Step 2: Find a common denominator. Since 6 is a multiple of 3, we can use 6 as the common denominator.
• Step 3: Adjust $\frac{1}{3}$ to have a denominator of 6. Multiply both the numerator and denominator of $\frac{1}{3}$ by 2 to get $\frac{2}{6}$.
• Step 4: Subtract the fractions now having the same denominator: $\frac{2}{6} - \frac{1}{6}$.
• Step 5: Subtract the numerators: $2 - 1 = 1$, keeping the denominator as 6, resulting in $\frac{1}{6}$.

Therefore, the solution to $\frac{1}{3} - \frac{1}{6}$ is $\frac{1}{6}$.

To solve the subtraction of fractions $\frac{2}{3} - \frac{2}{9}$, we will follow a step-by-step approach:

• Step 1: Identify the denominators of the fractions, which are 3 and 9.
• Step 2: Find the least common denominator (LCD) of 3 and 9. Since 9 is a multiple of 3, $\text{LCD} = 9$.
• Step 3: Convert each fraction to an equivalent fraction with this denominator.
• The fraction $\frac{2}{3}$ is converted to $\frac{6}{9}$ because $2 \times 3 = 6$ and $3 \times 3 = 9$.
• The fraction $\frac{2}{9}$ remains $\frac{2}{9}$ because it already has the denominator 9.
• Step 4: Subtract the numerators: $6 - 2 = 4$.
• Step 5: Place the result over the common denominator: $\frac{4}{9}$.

Thus, the result of the subtraction $\frac{2}{3} - \frac{2}{9}$ is $\frac{4}{9}$.

Therefore, the solution to the problem is $\frac{4}{9}$.

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

• Step 1: Find a common denominator for both fractions.
• Step 2: Convert the fractions to have the same denominator.
• Step 3: Perform the subtraction with the converted fractions.
• Step 4: Simplify the result, if needed.

Now, let's work through each step:
Step 1: The problem gives us the fractions $\frac{1}{2}$ and $\frac{2}{8}$. The denominator $2$ can be converted to $8$ (the denominator of the second fraction) by multiplying by 4.
Step 2: Convert $\frac{1}{2}$ to $\frac{4}{8}$, since $\frac{1 \times 4}{2 \times 4} = \frac{4}{8}$. Now both fractions have a denominator of 8.
Step 3: Perform the subtraction: $\frac{4}{8} - \frac{2}{8} = \frac{4 - 2}{8} = \frac{2}{8}$.
Step 4: Simplify $\frac{2}{8}$ by dividing both numerator and denominator by 2: $\frac{2 \div 2}{8 \div 2} = \frac{1}{4}$.

Therefore, the solution to the problem is $\frac{1}{4}$.

To solve the subtraction $\frac{1}{2} - \frac{1}{4}$, follow these steps:

• Step 1: Identify a common denominator. Here, the least common denominator of 2 and 4 is 4.
• Step 2: Convert $\frac{1}{2}$ to a fraction with denominator 4. This involves multiplying both the numerator and denominator by 2: $\frac{1}{2} = \frac{2}{4}$.
• Step 3: $\frac{1}{4}$ already has the denominator of 4, so we don't need any adjustment there.
• Step 4: Subtract the numerators: $2 - 1 = 1$.
• Step 5: Write the result over the common denominator: $\frac{1}{4}$.

Therefore, the solution to $\frac{1}{2} - \frac{1}{4}$ is $\frac{1}{4}$.

To solve the problem $\frac{5}{8} - \frac{1}{4}$, we need to follow these steps:

• Step 1: Identify a common denominator. Here, since $\frac{1}{4}$ shares the denominator 4 with 8, the least common denominator (LCD) is 8.
• Step 2: Convert $\frac{1}{4}$ to have the denominator of 8 by multiplying both the numerator and denominator by 2. Thus, $\frac{1}{4} = \frac{2}{8}$.
• Step 3: Perform the subtraction: $\frac{5}{8} - \frac{2}{8} = \frac{3}{8}$.

Thus, the result of the subtraction $\frac{5}{8} - \frac{1}{4}$ is $\frac{3}{8}$.

Therefore, the solution to the problem is $\frac{3}{8}$.

Let's begin by identifying the lowest common denominator between 5 and 10.

In order to determine the lowest common denominator, we must find a number that is divisible by both 5 and 10.

In this case, the common denominator is 10.

Now let's proceed to multiply each fraction by the appropriate number to reach the denominator 10.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{4\times2}{5\times2}-\frac{3\times1}{10\times1}=\frac{8}{10}-\frac{3}{10}$

Finally let's subtract as follows:

$\frac{8-3}{10}=\frac{5}{10}$

Let's begin by determining the lowest common denominator between 5 and 10.

In order to identify the lowest common denominator, we must find a number that is divisible by both 5 and 10.

In this case, the common denominator is 10

Let's proceed to multiply each fraction by the appropriate number in order to reach the denominator 10.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{4\times2}{5\times2}-\frac{5\times1}{10\times1}=\frac{8}{10}-\frac{5}{10}$

Finally let's subtract as follows:

$\frac{8-5}{10}=\frac{3}{10}$

Let's begin by identifying the lowest common denominator between 5 and 10.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 5 and 10.

In this case, the common denominator is 10.

Let's proceed to multiply each fraction by the appropriate number to reach the denominator 10.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{3\times2}{5\times2}-\frac{3\times1}{10\times1}=\frac{6}{10}-\frac{3}{10}$

Finally let's subtract as follows:

$\frac{6-3}{10}=\frac{3}{10}$