Subtraction of Fractions: More than two fractions

Let's try to identify the lowest common denominator between 10 and 5.

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

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 1

We'll multiply the second fraction by 2

We'll multiply the third fraction by 1

$\frac{8\times1}{10\times1}-\frac{1\times2}{5\times2}-\frac{2\times1}{10\times1}=\frac{8}{10}-\frac{2}{10}-\frac{2}{10}$

Finally let's subtract as follows:

$\frac{8-2-2}{10}=\frac{6-2}{10}=\frac{4}{10}$

Let's try to find the least common denominator between 10 and 5

To find the least common denominator, we need to find a number that is divisible by both 10 and 5

In this case, the common denominator is 10

Now we'll multiply each fraction by the appropriate number to reach the denominator 10

We'll multiply the first fraction by 1

We'll multiply the second fraction by 2

We'll multiply the third fraction by 1

$\frac{4\times1}{10\times1}-\frac{1\times2}{5\times2}-\frac{1\times1}{10\times1}=\frac{4}{10}-\frac{2}{10}-\frac{1}{10}$

Now we'll subtract and get:

$\frac{4-2-1}{10}=\frac{2-1}{10}=\frac{1}{10}$

Let's try to find the least common multiple (LCM) between 5, 15, and 3

To find the least common multiple, we need to find a number that is divisible by 5, 15, and 3

In this case, the least common multiple is 15

Now we'll multiply each fraction by the appropriate number to reach the denominator 15

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

We'll multiply the third fraction by 5

$\frac{8\times3}{5\times3}-\frac{2\times1}{15\times1}-\frac{2\times5}{3\times5}=\frac{24}{15}-\frac{2}{15}-\frac{10}{15}$

Now let's subtract:

$\frac{24-2-10}{15}=\frac{22-10}{15}=\frac{12}{15}$

Let's divide both numerator and denominator by 3 and we get:

$\frac{12:3}{15:3}=\frac{4}{5}$

Let's try to find the least common denominator between 5 and 15 and 3

To find the least common denominator, we need to find a number that is divisible by 5, 15, and 3

In this case, the common denominator is 15

Now we'll multiply each fraction by the appropriate number to reach the denominator 15

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

We'll multiply the third fraction by 5

$\frac{7\times3}{5\times3}-\frac{2\times1}{15\times1}-\frac{2\times5}{3\times5}=\frac{21}{15}-\frac{2}{15}-\frac{10}{15}$

Now let's subtract:

$\frac{21-2-10}{15}=\frac{19-10}{15}=\frac{9}{15}$

We'll divide both the numerator and denominator by 3 and get:

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

Let's try to find the least common denominator between 3, 6, and 12

To find the least common denominator, we need to find a number that is divisible by 3, 6, and 12

In this case, the common denominator is 12

Now we'll multiply each fraction by the appropriate number to reach the denominator 12

We'll multiply the first fraction by 4

We'll multiply the second fraction by 2

We'll multiply the third fraction by 1

$\frac{2\times4}{3\times4}-\frac{1\times2}{6\times2}-\frac{3\times1}{12\times1}=\frac{8}{12}-\frac{2}{12}-\frac{3}{12}$

Now let's subtract:

$\frac{8-2-3}{12}=\frac{6-3}{12}=\frac{3}{12}$

Let's divide both numerator and denominator by 3 and we get:

$\frac{3:3}{12:3}=\frac{1}{4}$

Let's try to find the lowest common denominator between 6, 4, and 12

To find the lowest common denominator, we need to find a number that is divisible by 6, 4, and 12

In this case, the common denominator is 12

Now we'll multiply each fraction by the appropriate number to reach the denominator 12

We'll multiply the first fraction by 2

We'll multiply the second fraction by 3

We'll multiply the third fraction by 1

$\frac{5\times2}{6\times2}-\frac{2\times3}{4\times3}-\frac{3\times1}{12\times1}=\frac{10}{12}-\frac{6}{12}-\frac{3}{12}$

Now we'll subtract and get:

$\frac{10-6-3}{12}=\frac{4-3}{12}=\frac{1}{12}$

Let's try to find the lowest common denominator between 12, 3, and 6

To find the lowest common denominator, we need to find a number that is divisible by 12, 3, and 6

In this case, the common denominator is 12

Now we'll multiply each fraction by the appropriate number to reach the denominator 12

We'll multiply the first fraction by 1

We'll multiply the second fraction by 4

We'll multiply the third fraction by 2

$\frac{10\times1}{12\times1}-\frac{2\times4}{3\times4}-\frac{1\times2}{6\times2}=\frac{10}{12}-\frac{8}{12}-\frac{2}{12}$

Now let's subtract:

$\frac{10-8-2}{12}=\frac{2-2}{12}=\frac{0}{12}$

We'll divide both the numerator and denominator by 0 and get:

$\frac{0}{12}=0$

Let's try to find the lowest common multiple of 3, 6 and 12

To find the lowest common multiple, we find a number that is divisible by 3, 6 and 12

In this case, the common multiple is 12

Now let's multiply each number in the appropriate multiple to reach the multiple of 12

We will multiply the first number by 4

We will multiply the second number by 2

We will multiply the third number by 1

$\frac{2\times4}{3\times4}-\frac{1\times2}{6\times2}-\frac{6\times1}{12\times1}=\frac{8}{12}-\frac{2}{12}-\frac{6}{12}$

Now let's subtract:

$\frac{8-2-6}{12}=\frac{6-6}{12}=\frac{0}{12}$

We will divide the numerator and the denominator by 0 and get:

$\frac{0}{12}=0$

Let's try to find the least common denominator between 6, 3, and 12

To find the least common denominator, we need to find a number that is divisible by 6, 3, and 12

In this case, the common denominator is 12

Now we'll multiply each fraction by the appropriate number to reach the denominator 12

We'll multiply the first fraction by 2

We'll multiply the second fraction by 4

We'll multiply the third fraction by 1

$\frac{3\times2}{6\times2}-\frac{1\times4}{3\times4}-\frac{1\times1}{12\times1}=\frac{6}{12}-\frac{4}{12}-\frac{1}{12}$

Now let's subtract:

$\frac{6-4-1}{12}=\frac{2-1}{12}=\frac{1}{12}$

Let's try to find the least common denominator between 2 and 8 and 4

To find the least common denominator, we need to find a number that is divisible by 2, 8, and 4

In this case, the common denominator is 8

Now we'll multiply each fraction by the appropriate number to reach the denominator 8

We'll multiply the first fraction by 4

We'll multiply the second fraction by 1

We'll multiply the third fraction by 2

$\frac{3\times4}{2\times4}-\frac{5\times1}{8\times1}-\frac{1\times2}{4\times2}=\frac{12}{8}-\frac{5}{8}-\frac{2}{8}$

Now let's subtract:

$\frac{12-5-2}{8}=\frac{7-2}{8}=\frac{5}{8}$

Let's try to find the lowest common denominator between 6, 3, and 12

To find the lowest common denominator, we need to find a number that is divisible by 6, 3, and 12

In this case, the common denominator is 12

Now we'll multiply each fraction by the appropriate number to reach the denominator 12

We'll multiply the first fraction by 2

We'll multiply the second fraction by 4

We'll multiply the third fraction by 1

$\frac{4\times2}{6\times2}-\frac{1\times4}{3\times4}-\frac{1\times1}{12\times1}=\frac{8}{12}-\frac{4}{12}-\frac{1}{12}$

Now let's subtract:

$\frac{8-4-1}{12}=\frac{4-1}{12}=\frac{3}{12}$

Let's divide both numerator and denominator by 3 and we get:

$\frac{3:3}{12:3}=\frac{1}{4}$

To solve the problem $\frac{4}{5} - \frac{3}{10} - \frac{1}{5}$, we'll perform the following steps:

• Step 1: Find the common denominator of the fractions involved in subtraction.
• Step 2: Convert each fraction to have this common denominator.
• Step 3: Subtract the fractions and simplify the result.

Let's work through each step:

Step 1: Identify a common denominator for the fractions. The denominators are 5, 10, and 5. The least common multiple of these numbers is 10.

Step 2: Convert each fraction to have the common denominator of 10:

• $\frac{4}{5}$ can be rewritten as $\frac{8}{10}$ because multiplying both the numerator and the denominator by 2 gives $\frac{8}{10}$.
• $\frac{3}{10}$ already has the denominator 10, so it remains $\frac{3}{10}$.
• $\frac{1}{5}$ can be rewritten as $\frac{2}{10}$ because multiplying both the numerator and the denominator by 2 gives $\frac{2}{10}$.

Step 3: Subtract the fractions:

$\frac{8}{10} - \frac{3}{10} - \frac{2}{10} = \left(\frac{8 - 3 - 2}{10}\right) = \frac{3}{10}$.

Thus, the result of the subtraction $\frac{4}{5} - \frac{3}{10} - \frac{1}{5}$ is $\frac{3}{10}$.

To solve the subtraction of three fractions, follow these steps:

• Step 1: Identify the denominators of the fractions: 6, 3, and 12.
• Step 2: Determine the least common denominator (LCD), which is the least common multiple of 6, 3, and 12. The LCD is 12.
• Step 3: Convert each fraction to an equivalent fraction with the LCD of 12.
• $\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}$
• $\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$
• $\frac{2}{12}$ remains $\frac{2}{12}$.
• Step 4: Perform the subtraction with these equivalent fractions:
  $\frac{10}{12} - \frac{4}{12} - \frac{2}{12}$.
• Step 5: Subtract the fractions:
  $\frac{10 - 4 - 2}{12} = \frac{4}{12}$.
• Step 6: Simplify the resulting fraction 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 the exercise $\frac{2}{3} - \frac{1}{15} - \frac{2}{5}$, we proceed as follows:

• Step 1: Determine the least common denominator (LCD) for the fractions. The denominators are 3, 15, and 5. The LCD of these numbers is 15.
• Step 2: Convert each fraction to an equivalent fraction with the common denominator of 15.
• $\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}$
• $\frac{1}{15}$ remains as $\frac{1}{15}$ since it is already using the common denominator.
• $\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}$
• Step 3: Perform the subtraction by subtracting the numerators while keeping the denominator the same.
• $\frac{10}{15} - \frac{1}{15} = \frac{9}{15}$
• $\frac{9}{15} - \frac{6}{15} = \frac{3}{15}$
• Step 4: Simplify the resulting fraction, $\frac{3}{15}$, by dividing the numerator and the denominator by their greatest common divisor (GCD), which is 3.
• $\frac{3}{15} = \frac{3 \div 3}{15 \div 3} = \frac{1}{5}$

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

To solve this problem, we will follow these steps:

• Step 1: Find the least common denominator of the fractions involved.
• Step 2: Rewrite each fraction using this common denominator.
• Step 3: Subtract the fractions sequentially.

Now, let's work through each step:

First, we determine the least common denominator (LCD) of the fractions $\frac{1}{2}$, $\frac{1}{8}$, and $\frac{1}{4}$. The denominators are 2, 8, and 4. The least common multiple of these numbers is 8. Thus, the LCD is 8.

Next, we rewrite each fraction with the common denominator of 8:

• $\frac{1}{2} = \frac{4}{8}$
• $\frac{1}{8} = \frac{1}{8}$
• $\frac{1}{4} = \frac{2}{8}$

Now, we perform the subtraction:

$\frac{1}{2} - \frac{1}{8} - \frac{1}{4} = \frac{4}{8} - \frac{1}{8} - \frac{2}{8}$

First, subtract $\frac{1}{8}$ from $\frac{4}{8}$:

$\frac{4}{8} - \frac{1}{8} = \frac{3}{8}$

Then, subtract $\frac{2}{8}$ from $\frac{3}{8}$:

$\frac{3}{8} - \frac{2}{8} = \frac{1}{8}$

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

To solve this problem, we need to subtract three fractions: $\frac{1}{2} - \frac{1}{6} - \frac{3}{12}$.

First, let's find the least common denominator (LCD) for the fractions. The denominators are 2, 6, and 12. The smallest number that all these denominators divide evenly into is 12, so the LCD is 12.

Next, convert each fraction to have 12 as the denominator:

• $\frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12}$
• $\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}$
• $\frac{3}{12}$ is already with denominator 12

Now, perform the subtraction using these equivalent fractions:

$\frac{6}{12} - \frac{2}{12} - \frac{3}{12}$

Subtract the fractions in sequence while keeping the common denominator:

$\frac{6}{12} - \frac{2}{12} = \frac{4}{12}$

Then, $\frac{4}{12} - \frac{3}{12} = \frac{1}{12}$

The fraction $\frac{1}{12}$ is already in its simplest form.

Therefore, the solution to the problem is $\frac{1}{12}$.

To solve $\frac{11}{12} - \frac{1}{3} - \frac{1}{6}$, we will follow these steps:

• Step 1: Identify the Least Common Denominator (LCD)
• Step 2: Convert each fraction to an equivalent fraction with the LCD
• Step 3: Perform the subtraction

Now, let's work through these steps:

Step 1: Identify the Least Common Denominator (LCD)
The denominators are 12, 3, and 6. The least common denominator is 12.

Step 2: Convert each fraction
- The fraction $\frac{11}{12}$ already has a denominator of 12.
- Convert $\frac{1}{3}$ to a denominator of 12: $\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$.
- Convert $\frac{1}{6}$ to a denominator of 12: $\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}$.

Step 3: Perform the subtraction
Now that the fractions have the same denominator, subtract the numerators:
$\frac{11}{12} - \frac{4}{12} - \frac{2}{12} = \frac{11 - 4 - 2}{12} = \frac{5}{12}$.

Therefore, the solution to the problem is $\frac{5}{12}$.

To solve the problem $\frac{9}{10} - \frac{1}{5} - \frac{4}{10}$, we follow these steps:

• Step 1: Identify the common denominator.
• Step 2: Convert all fractions to have this common denominator.
• Step 3: Perform the subtraction.
• Step 4: Simplify the resulting fraction, if necessary.

Now, let's apply these steps:

Step 1: The common denominator for the fractions is 10 since this is a multiple of both 10 and 5.

Step 2: Convert $\frac{1}{5}$ to a fraction with denominator 10. To do this, multiply both the numerator and the denominator by 2:

$\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}$

Now, our expression is $\frac{9}{10} - \frac{2}{10} - \frac{4}{10}$.

Step 3: Subtract the fractions:

First, subtract $\frac{2}{10}$ from $\frac{9}{10}$:

$\frac{9}{10} - \frac{2}{10} = \frac{9 - 2}{10} = \frac{7}{10}$

Next, subtract $\frac{4}{10}$ from $\frac{7}{10}$:

$\frac{7}{10} - \frac{4}{10} = \frac{7 - 4}{10} = \frac{3}{10}$

Step 4: The fraction $\frac{3}{10}$ is already in its simplest form.

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

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

• Step 1: Identify the least common denominator (LCD).
• Step 2: Convert each fraction to have the common denominator.
• Step 3: Subtract the numerators and simplify the final result.

Now, let's work through each step:
Step 1: The denominators are $6$, $4$, and $12$. The smallest number that is a multiple of all these denominators is $12$, so our LCD is $12$.
Step 2: Convert each fraction to have a denominator of $12$:

• $\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}$
• $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$
• $\frac{3}{12}$ already has the denominator $12$.

Step 3: Subtract the fractions, now rewritten as having the same denominator:

$\frac{10}{12} - \frac{3}{12} - \frac{3}{12}$.

Subtract the numerators:

The resulting fraction is $\frac{4}{12}$.

We simplify $\frac{4}{12}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $4$:

$\frac{4 \div 4}{12 \div 4} = \frac{1}{3}$.

Therefore, the simplified result of the operation is $\frac{1}{3}$.

To solve the problem $\frac{3}{2} - \frac{3}{8} - \frac{1}{4}$, follow these steps:

• Step 1: Find the Least Common Denominator (LCD): The denominators are 2, 8, and 4. The smallest number that all these can divide into is 8. So, the LCD is 8.
• Step 2: Convert each fraction to have a denominator of 8:
  • $\frac{3}{2}$ becomes $\frac{12}{8}$ because $\frac{3}{2} \times \frac{4}{4} = \frac{12}{8}$.
  • $\frac{3}{8}$ is already with a denominator of 8.
  • $\frac{1}{4}$ becomes $\frac{2}{8}$ because $\frac{1}{4} \times \frac{2}{2} = \frac{2}{8}$.
• Step 3: Perform the Subtraction:
  • First subtract the fractions: $\frac{12}{8} - \frac{3}{8} = \frac{9}{8}$.
  • Then, subtract $\frac{2}{8}$ from the result: $\frac{9}{8} - \frac{2}{8} = \frac{7}{8}$.
• Step 4: Simplify the Result: The fraction $\frac{7}{8}$ is already in its simplest form.

Therefore, the solution to the problem is $\frac{7}{8}$.