Addition of Fractions - Examples, Exercises and Solutions

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

• Step 1: Identify that both fractions have the same denominator.
• Step 2: Add their numerators.
• Step 3: Write the result as a single fraction and simplify if needed.

Now, let's work through each step:
Step 1: Both fractions are $\frac{1}{2}$, which means they have the same denominator, 2.
Step 2: Add the numerators: $1 + 1 = 2$.
Step 3: Write the result as $\frac{2}{2}$. Simplifying $\frac{2}{2}$ gives us $1$.

Therefore, the solution to the problem is 1.

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

• Step 1: Recognize that both fractions share the same denominator, which is 3.
• Step 2: Add the numerators: $1 + 1 = 2$.
• Step 3: Keep the common denominator of 3, resulting in the fraction $\frac{2}{3}$.

Now, let's work through each step:
Step 1: We observe that the denominators of both fractions are 3, so we do not need to change them.
Step 2: We add the numerators. Each fraction has a numerator of 1, so adding them gives us 2.
Step 3: We write the sum of the numerators over the common denominator, giving us $\frac{2}{3}$.

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

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

• Step 1: Identify the numerators and denominators of the given fractions.
• Step 2: Add the numerators while keeping the same denominator.

Now, let's work through each step:
Step 1: The given fractions are $\frac{1}{4}$ and $\frac{1}{4}$. Both have a denominator of 4 and a numerator of 1.
Step 2: We will add the numerators: $1 + 1 = 2$, and keep the denominator as 4. This results in $\frac{2}{4}$.

Therefore, the solution to the problem is $\frac{2}{4}$. Looking at the choices provided, this matches choice 3: $\frac{2}{4}$.

To solve the problem $\frac{1}{5} + \frac{0}{5}$, we will follow these steps:

• Step 1: Observe that both fractions have the same denominator which is 5.
• Step 2: Add the numerators: $1 + 0 = 1$.
• Step 3: Keep the denominator unchanged, which is 5.

Now, performing these steps:
- Since the denominators are the same, we simply add the numerators: $1 + 0 = 1$.
- Therefore, the resulting fraction is $\frac{1}{5}$.

Hence, the answer to the problem is $\frac{1}{5}$.

To solve this problem, we'll add two fractions with a common denominator:

• Step 1: Identify the numerators and the common denominator of the fractions.
• Step 2: Add the numerators, keeping the denominator unchanged.

Let's do this for our given fractions:

We have the fractions $\frac{1}{5}$ and $\frac{1}{5}$. Both have the same denominator, which is 5.
Step 1: The numerators are 1 and 1, and the common denominator is 5.

Step 2: Add the numerators while keeping the denominator same:
$\frac{1}{5} + \frac{1}{5} = \frac{1 + 1}{5} = \frac{2}{5}$.

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

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

• Step 1: Identify the common denominator.
• Step 2: Add the numerators and keep the common denominator.

Now, let's work through each step:
Step 1: Both fractions $\frac{1}{5}$ and $\frac{3}{5}$ have the common denominator of 5.
Step 2: Add the numerators: $1 + 3 = 4$.
Thus, we get $\frac{4}{5}$.

Therefore, the solution to the problem is $\frac{4}{5}$. This corresponds to choice 4.

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

• Step 1: Identify the given fractions and their common denominator.
• Step 2: Add the numerators and maintain the same denominator.
• Step 3: Simplify the resulting fraction if necessary.

Now, let's work through each step:
Step 1: The fractions given are $\frac{1}{5}$ and $\frac{3}{5}$. They have a common denominator of 5.
Step 2: To add these fractions, we compute $\frac{1}{5} + \frac{3}{5} = \frac{1 + 3}{5}$.
Step 3: Simplifying the fraction, we get $\frac{4}{5}$.

Therefore, the solution to the problem is $\frac{4}{5}$.

To solve this problem, we need to add the fractions $\frac{1}{5}$ and $\frac{4}{5}$. Let's follow these steps:

• Step 1: Ensure the fractions have the same denominator.
  Both fractions, $\frac{1}{5}$ and $\frac{4}{5}$, already have the same denominator, which is 5.
• Step 2: Add the numerators while keeping the denominator the same.
  Compute $1 + 4 = 5$. This gives us the new fraction $\frac{5}{5}$.
• Step 3: Simplify the fraction if needed.
  The fraction $\frac{5}{5}$ simplifies to 1, since 5 divided by 5 is 1.
• Step 4: Confirm against the answer choices.
  The simplified result 1 corresponds to choice number 2, which is 1.

Therefore, the solution to the problem is 1.

To solve this problem, let's add the fractions $\frac{1}{6}$ and $\frac{1}{6}$.

• Step 1: Confirm that the denominators are the same, which they are. Both fractions have a denominator of 6.
• Step 2: Add the numerators together: $1 + 1 = 2$.
• Step 3: Write the result as a fraction over the common denominator: $\frac{2}{6}$.

Thus, the sum of $\frac{1}{6} + \frac{1}{6}$ is $\frac{2}{6}$.

Therefore, the correct answer is choice 3: $\frac{2}{6}$.

To solve this problem, let's add the two fractions: $\frac{1}{6} + \frac{3}{6}$.

Step 1: Confirm the denominators are the same. In this case, both fractions have the denominator of 6.

Step 2: Add the numerators while keeping the common denominator:

• Numerators: $1 + 3 = 4$
• Denominator: 6

Step 3: Combine the result from Step 2:

$\frac{1}{6} + \frac{3}{6} = \frac{4}{6}$

Thus, the solution to the problem is $\frac{4}{6}$.

To solve this problem, we will follow these steps:

• Step 1: Identify the denominators of the fractions. Both $\frac{2}{5}$ and $\frac{3}{5}$ have the denominator 5.
• Step 2: When adding fractions with the same denominator, we only need to add the numerators.
• Step 3: Calculate $\frac{2}{5} + \frac{3}{5} = \frac{2 + 3}{5} = \frac{5}{5}$.
• Step 4: Simplify $\frac{5}{5}$, which equals 1.

Therefore, the solution to the problem is 1.

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

• Step 1: Confirm that the denominators are the same.
• Step 2: Add the numerators while keeping the denominator unchanged.
• Step 3: Write down the result as a new fraction.

Now, let's work through the solution:

Step 1: We observe that both fractions have the same denominator, which is 6.

Step 2: Add the numerators. The numerators are both 2, so $2 + 2 = 4$.

Step 3: Write the sum of the numerators over the common denominator:
$\frac{4}{6}$

Thus, the correct answer is $\frac{4}{6}$, which corresponds to choice 4.

To solve this problem, we need to add the fractions $\frac{2}{7}$ and $\frac{3}{7}$. Since both fractions have the same denominator, the process is simple:

• Step 1: Verify the fractions have a common denominator, which is 7.
• Step 2: Add the numerators together. Thus, $2 + 3 = 5$.
• Step 3: Keep the common denominator unchanged.

By adding the numerators $2$ and $3$, we obtain $5$, and the denominator remains $7$. Therefore, the resulting fraction is $\frac{5}{7}$.

This matches the given correct answer.

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

To solve this problem of adding fractions with like denominators, we will follow these steps:

• Step 1: Identify and confirm that the denominators of both fractions are the same. Here, both fractions have the denominator $7$.
• Step 2: Add the numerators of both fractions: $3 + 1 = 4$.
• Step 3: Keep the common denominator, which is $7$.
• Step 4: Write the resultant fraction as $\frac{4}{7}$.

Therefore, the sum of $\frac{3}{7}$ and $\frac{1}{7}$ is $\frac{4}{7}$.

To solve this problem, we'll follow a straightforward approach to adding fractions with like denominators:

Consider the fractions given: $\frac{3}{9}$ and $\frac{1}{9}$.

• Step 1: Since both fractions have the same denominator, we add their numerators: $3 + 1 = 4$.
• Step 2: Keep the denominator the same: 9.
• Step 3: Resulting in the fraction: $\frac{4}{9}$.

The computation confirms that the addition of these fractions results in $\frac{4}{9}$.

Therefore, the correct solution to the problem is $\frac{4}{9}$, which corresponds to choice 3.