Addition of Fractions: Fractions with common denominators

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'll follow these steps:

• Step 1: Identify the given fractions $\frac{4}{7}$ and $\frac{2}{7}$.
• Step 2: Since the denominators are the same, add the numerators directly.
• Step 3: Maintain the common denominator in the result.

Now, let's work through each step:
Step 1: The problem gives us the fractions $\frac{4}{7}$ and $\frac{2}{7}$.
Step 2: Add the numerators: $4 + 2 = 6$.
Step 3: The common denominator remains 7, so the result is $\frac{6}{7}$.

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

To solve the problem of adding the fractions $\frac{4}{11} + \frac{5}{11}$, we follow these steps:

• Step 1: Identify that both fractions have the same denominator of 11.
• Step 2: Since the denominators are the same, we can add their numerators directly:
  $4 + 5 = 9$.
• Step 3: Keep the common denominator, which remains as 11.

Now we combine these results to find the sum of the fractions:

$\frac{4}{11} + \frac{5}{11} = \frac{9}{11}$

The solution to the problem is $\frac{9}{11}$, which matches choice 3 in the provided options.

To solve the addition of the two fractions $\frac{4}{7} + \frac{3}{7}$, follow these steps:

• Step 1: Since both fractions have the same denominator, add the numerators directly: $4 + 3 = 7$.
• Step 2: Retain the common denominator: $7$.
• Step 3: The resulting fraction after addition is $\frac{7}{7}$.
• Step 4: Simplify the resulting fraction if possible. Since $\frac{7}{7} = 1$, the simplified result is $1$.

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, let's perform addition of fractions with like denominators:

• The given fractions are $\frac{0}{7}$ and $\frac{3}{7}$.
• Since they have the same denominator (7), we add the numerators: $0 + 3$.
• This results in a new numerator of 3, with the denominator remaining 7.
• Thus, the sum of the fractions is $\frac{3}{7}$.

Therefore, the solution to the problem is $\frac{3}{7}$.

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.

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

• Step 1: Identify that both fractions have the same denominator.
• Step 2: Add the numerators while keeping the denominator constant.
• Step 3: Simplify the resulting fraction if necessary.

Now, let's work through each step:
Step 1: Both fractions, $\frac{1}{7}$ and $\frac{2}{7}$, have a common denominator of 7.
Step 2: Add the numerators: $1 + 2 = 3$.
Step 3: Write the sum as a fraction with the denominator 7: $\frac{3}{7}$.

Therefore, the solution to the problem is $\frac{3}{7}$.

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 this problem, we'll apply the formula for adding fractions with a common denominator:

Step 1: Add the numerators of the fractions. Since the denominators are already equal, simply add:

• The numerators: $4 + 3 = 7$.

Step 2: Keep the denominator the same:

• The denominator remains 8, so the fraction becomes $\frac{7}{8}$.

Therefore, the sum of $\frac{4}{8} + \frac{3}{8}$ is $\frac{7}{8}$.

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, let us proceed with the following steps:

• Step 1: Identify the given fractions. We have two fractions: $\frac{4}{10}$ and $\frac{4}{10}$.
• Step 2: Recognize that both fractions have the same denominator, which makes the addition straightforward.
• Step 3: Add only their numerators while keeping the common denominator. Therefore, $4 + 4 = 8$.
• Step 4: Write the result with the calculated numerator and common denominator, obtaining $\frac{8}{10}$.

Based on our calculations, the sum of these fractions is $\frac{8}{10}$.

This answer matches choice 3 in the options provided.

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 the problem of adding $\frac{2}{7}$ and $\frac{2}{7}$, we proceed with the following steps:

Step 1: Identify the common denominator, which is 7 in this case. Since both fractions have the same denominator, we can apply the formula directly for adding fractions with a common denominator:

$\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$

Step 2: Add the numerators of the fractions. Combining the numerators, we have:

$2 + 2 = 4$

Step 3: Write the resulting fraction using the sum of the numerators and the common denominator. The resulting fraction becomes:

$\frac{4}{7}$

Conclusion: By adding the numerators and using the shared denominator, the sum of $\frac{2}{7} + \frac{2}{7}$ is $\frac{4}{7}$.

The correct answer choice is $\frac{4}{7}$, and this corresponds to choice 4.

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

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 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, 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: 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'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 $\frac{3}{5}$.