Addition of Fractions: Fractions with common denominators

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 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 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 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 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 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 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 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 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 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 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, 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 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 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 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 add the fractions $\frac{2}{8}$ and $\frac{3}{8}$. Because the fractions have the same denominator, we use the following approach:

• Step 1: Confirm the denominators are the same. In this case, both are 8.
• Step 2: Add the numerators: $2 + 3 = 5$.
• Step 3: Combine the result into a single fraction using the common denominator:
  $\frac{5}{8}$.

Therefore, the solution to the problem is $\frac{5}{8}$.

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 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: $\frac{10}{11}$.

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 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 $\frac{3}{10}$.