All Operations in Fractions: More than two fractions

To solve this problem, let's multiply the given fractions step-by-step:

• Step 1: Multiply the numerators of the fractions together: $2 \times 1 \times 4 = 8$
• Step 2: Multiply the denominators of the fractions together: $3 \times 2 \times 5 = 30$
• Step 3: Form the fraction using the results from Steps 1 and 2: $\frac{8}{30}$
• Step 4: Simplify the fraction $\frac{8}{30}$: - Find the greatest common divisor (GCD) of 8 and 30, which is 2. $\frac{8 \div 2}{30 \div 2} = \frac{4}{15}$

The simplified fraction is $\frac{4}{15}$.

Therefore, the correct result of the multiplication is $\frac{4}{15}$.

To solve this problem, I will follow these clear steps:

• Step 1: Multiply the numerators of the fractions: $2 \times 2 \times 1$.
• Step 2: Multiply the denominators of the fractions: $4 \times 3 \times 2$.
• Step 3: Simplify the resulting fraction.

Let's work through each step:

Step 1: Multiply the numerators: $2 \times 2 \times 1 = 4$.

Step 2: Multiply the denominators: $4 \times 3 \times 2 = 24$.

Step 3: Combine these results to write the product as a fraction:

$\frac{4}{24}$.

We need to simplify this fraction:

Find the greatest common divisor (GCD) of 4 and 24, which is 4.

Divide both the numerator and the denominator by their GCD:

$\frac{4}{24} = \frac{4 \div 4}{24 \div 4} = \frac{1}{6}$.

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

To solve the multiplication of the fractions $\frac{4}{3}$, $\frac{1}{2}$, and $\frac{6}{5}$, we'll follow these steps:

• Step 1: Multiply the numerators: $4 \times 1 \times 6 = 24$.
• Step 2: Multiply the denominators: $3 \times 2 \times 5 = 30$.
• Step 3: Form the new fraction: $\frac{24}{30}$.
• Step 4: Simplify the fraction $\frac{24}{30}$:
  Find the greatest common divisor (GCD) of 24 and 30, which is 6.
  Divide both the numerator and the denominator by their GCD:
  $\frac{24 \div 6}{30 \div 6} = \frac{4}{5}$.

Therefore, the product of $\frac{4}{3} \times \frac{1}{2} \times \frac{6}{5} = \frac{4}{5}$.

The correct choice from the given options is : $\frac{4}{5}$.

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

• Step 1: Multiply the numerators
• Step 2: Multiply the denominators
• Step 3: Simplify the resulting fraction
• Step 4: Verify the solution with the given choices

Now, let's work through each step:

Step 1: Multiply the numerators:
$3 \times 1 \times 1 = 3$.

Step 2: Multiply the denominators:
$4 \times 2 \times 2 = 16$.

Step 3: Write the resulting fraction:
$\frac{3}{16}$.

Step 4: Look at the multiple-choice list provided. Our answer, $\frac{3}{16}$, matches choice 1.

The resulting fraction is already in its simplest form. Therefore, the solution to the problem is $\frac{3}{16}$.

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

• Step 1: Multiply the numerators together.
• Step 2: Multiply the denominators together.
• Step 3: Simplify the resulting fraction.

Let's perform these calculations:
Step 1: Multiply the numerators: $2 \times 1 \times 2 = 4$.
Step 2: Multiply the denominators: $5 \times 2 \times 3 = 30$.
Step 3: Form the resulting fraction: $\frac{4}{30}$. Now, simplify the fraction

To simplify $\frac{4}{30}$, find the greatest common divisor (GCD) of 4 and 30, which is 2.
Thus, divide both the numerator and the denominator by 2:

$\frac{4 \div 2}{30 \div 2} = \frac{2}{15}$.

Therefore, the solution to the problem is $\frac{2}{15}$.

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

• Step 1: Multiply the numerators of the fractions together.
• Step 2: Multiply the denominators of the fractions together.
• Step 3: Simplify the resulting fraction, if possible.

Now, let's work through each step:
Step 1: Multiply the numerators: $2 \times 3 \times 4 = 24$.
Step 2: Multiply the denominators: $3 \times 4 \times 5 = 60$.
Step 3: The resulting fraction is $\frac{24}{60}$. Simplify by finding the greatest common divisor of 24 and 60, which is 12.

Divide both the numerator and the denominator by 12:
Numerator: $\frac{24}{12} = 2$
Denominator: $\frac{60}{12} = 5$
Thus, the simplified fraction is $\frac{2}{5}$.

Therefore, the solution to the problem is $\frac{2}{5}$.

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

• Step 1: Multiply the numerators of the given fractions.

• Step 2: Multiply the denominators of the given fractions.

• Step 3: Combine the results into a single fraction.

• Step 4: Simplify the fraction if needed.

Now, let's work through each step:
Step 1: Multiply the numerators: $3 \times 1 \times 1 = 3$.
Step 2: Multiply the denominators: $4 \times 2 \times 6 = 48$.
Step 3: The resulting fraction is $\frac{3}{48}$.

Therefore, the solution to the problem is $\frac{3}{48}$.

The problem requires multiplying the fractions $\frac{5}{4}$, $\frac{1}{2}$, and $\frac{3}{6}$.

Step 1: Multiply the numerators.

We have: $5 \times 1 \times 3 = 15$.

Step 2: Multiply the denominators.

We have: $4 \times 2 \times 6 = 48$.

Step 3: Form the fraction from results of the two steps above.

The product of these fractions is $\frac{15}{48}$.

Step 4: Simplify the fraction.

To simplify $\frac{15}{48}$, we need to find the greatest common divisor (GCD) of 15 and 48. The GCD is 3.

Divide both the numerator and the denominator by their GCD:

$\frac{15 \div 3}{48 \div 3} = \frac{5}{16}$.

Thus, the simplified product of the fractions is $\frac{5}{16}$.

We can compare it against the given answer choices to confirm:

• Choice 1: $\frac{3}{16}$ - incorrect.
• Choice 2: $\frac{5}{16}$ - correct.
• Choice 3: $\frac{15}{48}$ - correct but not simplified.
• Choice 4: $\frac{15}{16}$ - incorrect.

The correct answer choice is Choice 2, $\frac{5}{16}$.

To solve this problem, we'll multiply the given fractions step-by-step:

Step 1: Multiply the numerators and the denominators.
Numerators: $1 \times 4 \times 3 = 12$.
Denominators: $4 \times 3 \times 2 = 24$.

Step 2: Write the new fraction from the results of multiplying the numerators and denominators.
$\frac{12}{24}$.

Step 3: Simplify the fraction by finding common factors in the numerator and denominator.
The greatest common divisor of 12 and 24 is 12. Divide both the numerator and the denominator by 12:
$\frac{12}{24} = \frac{12 \div 12}{24 \div 12} = \frac{1}{2}$.

Therefore, the product of the fractions $\frac{1}{4}$, $\frac{4}{3}$, and $\frac{3}{2}$ is $\frac{1}{2}$.

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

• Step 1: Multiply the numerators of all fractions.
• Step 2: Multiply the denominators of all fractions.
• Step 3: Simplify the resulting fraction.

Now, let's work through each step:
Step 1: Multiply the numerators: $1 \times 2 \times 7 = 14$.
Step 2: Multiply the denominators: $3 \times 4 \times 5 = 60$.
Step 3: The resulting fraction is $\frac{14}{60}$. Now, we simplify this fraction.

To simplify $\frac{14}{60}$, find the greatest common divisor (GCD) of 14 and 60, which is 2. Divide both the numerator and the denominator by their GCD:
$\frac{14}{60} = \frac{14 \div 2}{60 \div 2} = \frac{7}{30}$.

Therefore, the solution to the problem is $\frac{7}{30}$, which corresponds to choice 3.

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 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 $\frac{7}{8}$.

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

• Step 1: Identify the least common multiple (LCM) for the denominators 5, 15, and 3.
• Step 2: Convert each fraction to equivalent fractions with the common denominator.
• Step 3: Perform subtraction on these equivalent fractions.

Let's work through each step:

Step 1: The denominators are 5, 15, and 3. The LCM of these numbers is 15, as it is the smallest number that all denominators divide evenly.

Step 2:

• Convert $\frac{7}{5}$ to an equivalent fraction with a denominator of 15: $\frac{7}{5} = \frac{7 \times 3}{5 \times 3} = \frac{21}{15}$.
• $\frac{7}{15}$ already has the denominator 15.
• Convert $\frac{1}{3}$ to an equivalent fraction with a denominator of 15: $\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}$.

Step 3: Subtract the fractions:

$\frac{21}{15} - \frac{7}{15} - \frac{5}{15} = \frac{21 - 7 - 5}{15} = \frac{9}{15}.$

Simplify $\frac{9}{15}$ by dividing both numerator and denominator by their greatest common divisor (GCD), which is 3:

$\frac{9 \div 3}{15 \div 3} = \frac{3}{5}.$

Therefore, the solution to the problem is $\frac{3}{5}$.

To solve the expression $\frac{1}{2} - \frac{2}{8} + \frac{1}{4}$, we must first find a common denominator for the fractions involved.

Step 1: Identify a common denominator. The denominators are 2, 8, and 4. The smallest common multiple of these numbers is 8.

Step 2: Convert each fraction to have the common denominator of 8.

• The fraction $\frac{1}{2}$ can be written as $\frac{4}{8}$ because $1 \times 4 = 4$ and $2 \times 4 = 8$.
• The fraction $\frac{2}{8}$ is already expressed with 8 as the denominator.
• The fraction $\frac{1}{4}$ can be written as $\frac{2}{8}$ because $1 \times 2 = 2$ and $4 \times 2 = 8$.

Step 3: Substitute these equivalent fractions back into the original expression:

$\frac{4}{8} - \frac{2}{8} + \frac{2}{8}$

Step 4: Perform the subtraction and addition following the order of operations:

• Subtract: $\frac{4}{8} - \frac{2}{8} = \frac{2}{8}$
• Add: $\frac{2}{8} + \frac{2}{8} = \frac{4}{8}$

Step 5: Simplify the result:

$\frac{4}{8}$ simplifies to $\frac{1}{2}$ by dividing the numerator and denominator by 4.

Therefore, the value of the expression is $\frac{1}{2}$.