Addition of Fractions: Fractions with common denominators

To solve this problem, we'll follow a simple approach:

• Step 1: Identify the numerators and denominator. The fractions given are $\frac{3}{11}$ and $\frac{7}{11}$. The numerator of the first fraction is $3$, and the second is $7$. The shared denominator is $11$.
• Step 2: Add the numerators together. Calculate $3 + 7 = 10$.
• Step 3: Keep the common denominator $11$ unchanged.

Thus, the sum of the fractions is $\frac{10}{11}$.

We compare this to the given choices:

• Choice 1: $1$
• Choice 2: $\frac{10}{11}$
• Choice 3: $\frac{8}{11}$
• Choice 4: $\frac{1}{11}$

The correct solution matches Choice 2: $\frac{10}{11}$.

Let's focus on the fraction of the fraction.
According to the order of operations rules, we'll solve from left to right, since it only contains addition and subtraction operations:

$5+3=8$

$8-2=6$

Now we'll get the fraction:

$\frac{6}{3}$

We'll reduce the numerator and denominator by 3 and get:

$\frac{2}{1}=2$

To solve this problem, we follow these steps:

• Step 1: Identify the numerators of the fractions. Here, both numerators are 1, as we have $\frac{1}{2}$ and $\frac{1}{2}$.
• Step 2: Add the numerators. We calculate $1 + 1 = 2$.
• Step 3: Keep the common denominator. The denominator remains 2.
• Step 4: Write the result as a single fraction. This gives us $\frac{2}{2}$.
• Step 5: Simplify the fraction. Since $\frac{2}{2}$ simplifies to 1, the final result is 1.

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

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

• Step 1: Identify the common denominator.
• Step 2: Add the numerators.
• Step 3: Simplify the resulting fraction if necessary.

Now, let's work through each step:
Step 1: Both fractions, $\frac{2}{3}$ and $\frac{1}{3}$, have the same denominator of 3.

Step 2: Add the numerators: $2 + 1 = 3$.

Step 3: Place the sum over the common denominator to get $\frac{3}{3}$.

The fraction $\frac{3}{3}$ simplifies to 1.

Therefore, the solution to the problem is $1$.

To solve this problem, we add the fractions $\frac{3}{13}$ and $\frac{7}{13}$ which have the same denominator.

When fractions have the same denominator, we simply add the numerators and place the sum over the common denominator.

$\frac{3}{13} + \frac{7}{13} = \frac{3 + 7}{13} = \frac{10}{13}$

The sum of the numerators is $10$ and the denominator remains $13$.

Therefore, the solution to the problem is $\frac{10}{13}$.

To solve this problem, we'll use the approach of adding fractions with a common denominator:

• Step 1: Identify that the fractions $\frac{1}{12}$ and $\frac{7}{12}$ have a common denominator, which is 12.
• Step 2: Since the denominators are the same, we add the numerators: $1 + 7 = 8$.
• Step 3: Keep the common denominator, which is 12.

Therefore, the sum of the fractions is $\frac{8}{12}$.

Thus, the solution to the problem is $\frac{8}{12}$.

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

• Step 1: Acknowledge that the fractions have a common denominator of 3.
• Step 2: Add the numerators of the two fractions.
• Step 3: Maintain the common denominator and simplify if necessary.

Now, let's work through each step:

Step 1: The fractions given are $\frac{1}{3}$ and $\frac{1}{3}$, both having the denominator 3.

Step 2: Add the numerators: $1 + 1 = 2$.

Step 3: The resulting fraction is $\frac{2}{3}$, with the denominator remaining unchanged. Simplification is not required.

Therefore, the solution to the problem is $\frac{2}{3}$.

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

• Step 1: Identify that both fractions, $\frac{4}{7}$ and $\frac{1}{7}$, have a common denominator of 7.
• Step 2: Add the numerators while keeping the denominator the same.

Let's work through each step:
Step 1: We have the two fractions $\frac{4}{7}$ and $\frac{1}{7}$. Both fractions share the denominator of 7.
Step 2: Add the numerators: $4 + 1 = 5$.
Thus, $\frac{4}{7} + \frac{1}{7} = \frac{5}{7}$.

Therefore, the solution to the problem is $\frac{5}{7}$.

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

• Step 1: Identify that both fractions have the same denominator of 7.
• Step 2: Add the numerators together: $1 + 5 = 6$.
• Step 3: Place the sum of the numerators over the common denominator.

Now, let's work through the solution:

Step 1: Since both fractions, $\frac{1}{7}$ and $\frac{5}{7}$, have the same denominator, we can directly apply the addition rule for fractions with a common denominator.

Step 2: Add the numerators 1 and 5. Performing this calculation: $1 + 5 = 6$.

Step 3: Place this result over the common denominator of 7. Therefore:

$\frac{1}{7} + \frac{5}{7} = \frac{1+5}{7} = \frac{6}{7}$

Therefore, the solution to the problem is $\frac{6}{7}$.

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

• Step 1: Identify the numbers to add: $\frac{1}{5}$ and $\frac{2}{5}$.
• Step 2: Confirm they have a common denominator.
• Step 3: Add their numerators.
• Step 4: Keep the common denominator.

Let's execute these steps:

Step 1: We have the fractions $\frac{1}{5}$ and $\frac{2}{5}$.

Step 2: Confirmed, both fractions have a common denominator, which is 5.

Step 3: Add the numerators: $1 + 2 = 3$.

Step 4: The denominator remains the same: 5.

Therefore, the sum of the fractions is $\frac{3}{5}$.

To solve the problem of adding the fractions $\frac{2}{6} + \frac{3}{6}$, we'll follow these steps:

• Step 1: Since both fractions have the same denominator (6), we can add the numerators directly.
• Step 2: Add the numerators: $2 + 3 = 5$.
• Step 3: Place the sum of the numerators over the common denominator: $\frac{5}{6}$.
• Step 4: The fraction $\frac{5}{6}$ is already in simplest form.

Therefore, the solution to the problem is $\frac{5}{6}$.

To solve this problem, follow these steps:

• Step 1: Identify the fractions to be added: $\frac{1}{7}$ and $\frac{3}{7}$.
• Step 2: Recognize that both fractions have the same denominator, which is 7.
• Step 3: Add the numerators: $1 + 3 = 4$.
• Step 4: Use the same denominator for the result: 7.

Therefore, the solution is that the sum of the two fractions is $\frac{4}{7}$.

The correct multiple-choice answer is : $\frac{4}{7}$

To solve the problem of adding $\frac{3}{9} + \frac{2}{9}$, follow these steps:

• Step 1: Since both fractions have the same denominator, we can add their numerators directly.
• Step 2: Add the numerators: $3 + 2 = 5$.
• Step 3: Use the common denominator for the sum: $\frac{5}{9}$.

Thus, the sum of $\frac{3}{9}$ and $\frac{2}{9}$ is $\frac{5}{9}$.

The correct choice from the provided options is $\frac{5}{9}$.

The final answer is: $\frac{5}{9}$.

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

• Step 1: Identify that both fractions have a common denominator.
• Step 2: Add the numerators while retaining the common denominator.

Let's work through each step:
Step 1: We have two fractions, $\frac{1}{10}$ and $\frac{2}{10}$, with the same denominator.

Step 2: We add their numerators:
$1 + 2 = 3$.
Keep the common denominator:
Thus, the fraction becomes $\frac{3}{10}$.

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

To solve this problem, we need to add the two fractions $\frac{1}{2} + \frac{1}{2}$. Since the fractions have the same denominator, we apply fraction addition rules by:

• Add the numerators: $1 + 1 = 2$.
• Keep the denominator the same: $2$.
• The resulting fraction is $\frac{2}{2}$.
• Simplify $\frac{2}{2}$ to $1$ since the numerator and denominator are equal.

Therefore, the sum of $\frac{1}{2} + \frac{1}{2}$ is $1$.

The correct answer is option 3: 1.

To solve this addition of fractions, we'll proceed with the following steps:

• Step 1: Observe that both fractions, $\frac{1}{4}$ and $\frac{2}{4}$, have the same denominator 4.
• Step 2: Apply the rule: Add the numerators and keep the denominator the same: $\frac{1}{4} + \frac{2}{4} = \frac{1+2}{4}$.
• Step 3: Compute the sum of the numerators: $1 + 2 = 3$.
• Step 4: Thus, the resulting fraction is $\frac{3}{4}$.

Therefore, the solution to the exercise $\frac{1}{4} + \frac{2}{4}$ is $\frac{3}{4}$.

To solve the problem of adding two fractions with a common denominator, we follow these steps:

• Step 1: Identify the numerators and denominators. Both fractions are $\frac{2}{5}$.
• Step 2: Since the denominators are the same, add the numerators: $2 + 2 = 4$.
• Step 3: Keep the common denominator: 5.
• Step 4: Form the result as a new fraction: $\frac{4}{5}$.

Therefore, the sum of $\frac{2}{5}$ and $\frac{2}{5}$ is $\frac{4}{5}$.

The correct choice from the provided options is $\frac{4}{5}$, which corresponds to choice 4.

To solve the problem of adding $\frac{1}{5}$ and $\frac{2}{5}$, follow these steps:

Step 1: Identify the denominators

Both fractions, $\frac{1}{5}$ and $\frac{2}{5}$, have the common denominator of 5. This simplifies the addition process since we only need to add the numerators.

Step 2: Add the numerators

When adding fractions with the same denominator, keep the denominator unchanged:

$\frac{1}{5} + \frac{2}{5} = \frac{1 + 2}{5}$

Step 3: Perform the addition

Add the numerators: $1 + 2 = 3$. So, the sum is:

$\frac{3}{5}$

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

To solve this problem, we follow these steps:

• Step 1: Confirm the fractions have the same denominator.
• Step 2: Add the numerators of the fractions.
• Step 3: Keep the common denominator the same.

Let's work through these steps:
Step 1: The two fractions are $\frac{3}{7}$ and $\frac{1}{7}$. Both have the same denominator of 7.
Step 2: Add the numerators, $3$ and $1$. This results in $3 + 1 = 4$.
Step 3: The denominator remains 7.
Thus, when we add the fractions, we get $\frac{4}{7}$.

Therefore, the solution to the problem is $\frac{4}{7}$.

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

• Step 1: Identify the common denominator for the fractions $\frac{1}{9}$ and $\frac{2}{9}$.
• Step 2: Add the numerators since the denominators are the same.
• Step 3: Write the sum over the common denominator.

Let's work through each step:

Step 1: Both fractions have a denominator of 9.

Step 2: Add the numerators: $1 + 2 = 3$.

Step 3: Write the result over the common denominator: $\frac{3}{9}$.

Therefore, the solution to the problem is $\frac{3}{9}$, which is choice 1.