Addition of Fractions - Examples, Exercises and Solutions

To solve this problem, let's follow these steps:

• Step 1: Identify that both fractions $\frac{2}{4}$ and $\frac{1}{4}$ have the same denominator.
• Step 2: Add the numerators together while keeping the denominator the same.
• Step 3: Simplify the resulting fraction if possible.

Now, let's perform these steps:

Step 1: The denominator for both fractions is 4, so we can proceed with addition.

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

Step 3: Place the result over the common denominator: $\frac{3}{4}$.

Therefore, the result of adding $\frac{2}{4} + \frac{1}{4}$ is $\frac{3}{4}$.

This matches the correct choice, which is $\frac{3}{4}$.

To solve the problem of adding the fractions $\frac{1}{4}$ and $\frac{3}{4}$, we can follow these steps:

• Step 1: Identify that both fractions share the same denominator of 4.
• Step 2: Add the numerators directly: $1 + 3 = 4$.
• Step 3: Retain the common denominator, giving us $\frac{4}{4}$.
• Step 4: Simplify the result, $\frac{4}{4} = 1$.

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

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

• Step 1: Verify that both fractions have the same denominator.
• Step 2: Add the numerators of the two fractions.
• Step 3: Retain the common denominator.
• Step 4: Simplify the resulting fraction if needed.

Let's work through each step to add $\frac{1}{2} + \frac{1}{2}$:
Step 1: Both fractions have the same denominator: 2.
Step 2: Add the numerators: $1 + 1 = 2$.
Step 3: The denominator remains the same: 2.
Now the sum is: $\frac{2}{2}$.
Step 4: Simplify if needed: $\frac{2}{2} = 1$.

Therefore, the solution to the problem is $1$, which corresponds to answer choice 2.

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

• Step 1: Ensure the fractions have the same denominator.
• Step 2: Add the numerators while keeping the common denominator.
• Step 3: Simplify the resulting fraction if needed.

Now, let's execute these steps:

Step 1: Both fractions, $\frac{4}{5}$ and $\frac{1}{5}$, have the denominator 5.
Step 2: Add the numerators: $4 + 1 = 5$. Keep the common denominator: $\frac{5}{5}$.
Step 3: Simplify the fraction $\frac{5}{5}$. Since the numerator and denominator are the same, this simplifies to 1.

Therefore, the answer is $1$.

To solve the problem of adding the fractions $\frac{2}{5}$ and $\frac{1}{5}$, we will utilize the fact that these fractions have the same denominator.

Here are the steps we will follow:

• Step 1: Identify the fractions to be added. We have $\frac{2}{5}$ and $\frac{1}{5}$.
• Step 2: Notice that both fractions have the same denominator, which is 5.
• Step 3: Add the numerators of the fractions while keeping the denominator unchanged.
• Step 4: The sum of the numerators is $2 + 1 = 3$.
• Step 5: Therefore, place the sum of the numerators over the common denominator 5, giving us $\frac{3}{5}$.

Thus, the sum of $\frac{2}{5}$ and $\frac{1}{5}$ is $\frac{3}{5}$.

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

• Step 1: Observe that the denominators of both fractions are identical, which is 6. This means we can add the fractions by simply adding their numerators.
• Step 2: Add the numerators: $2 + 3 = 5$.
• Step 3: Use the common denominator, which remains 6, to write the sum: $\frac{5}{6}$.

Therefore, the sum of $\frac{2}{6}$ and $\frac{3}{6}$ is $\frac{5}{6}$.

The correct answer to the problem is $\frac{5}{6}$.

To solve the problem of adding the fractions $\frac{2}{6} + \frac{1}{6}$, follow these steps:

• Step 1: Verify that both fractions have the same denominator.
• Step 2: Add the numerators of the fractions together, as they share the same denominator.
• Step 3: Write the result with the common denominator.

Let's work through these steps:

Step 1: Both fractions, $\frac{2}{6}$ and $\frac{1}{6}$, have the same denominator, 6.

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

Step 3: Place the result over the common denominator: $\frac{3}{6}$.

Therefore, the solution to the problem is $\frac{3}{6}$. This matches the answer choice: .

To solve the problem of adding $\frac{2}{7}$ and $\frac{1}{7}$, we will follow these steps:

• Step 1: Identify the common denominator. Since both fractions have the same denominator, 7, we can proceed to add the numerators directly.
• Step 2: Add the numerators: $2 + 1$.
• Step 3: Keep the common denominator in the result.

Now, let's work through each step:
Step 1: Both fractions, $\frac{2}{7}$ and $\frac{1}{7}$, have the denominator 7.
Step 2: Add the numerators: $2 + 1 = 3$.
Step 3: The fraction becomes $\frac{3}{7}$ by keeping the common denominator.

Thus, the sum of $\frac{2}{7}$ and $\frac{1}{7}$ is $\frac{3}{7}$.

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

• Step 1: Identify the fractions and check the denominators.
• Step 2: Add the numerators since the denominators are the same.
• Step 3: Reduce the fraction to its simplest form if possible.

Now, let's work through each step:
Step 1: We observe that the fractions are $\frac{3}{7}$ and $\frac{2}{7}$, both having the same denominator, 7.
Step 2: Since the denominators are the same, we can directly add the numerators: $3 + 2 = 5$.
Step 3: This results in the fraction $\frac{5}{7}$. As the fraction is already in its simplest form, no further simplification is needed.

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.
• Step 2: Add the numerators of the two fractions.
• Step 3: Keep the common denominator unchanged.
• Step 4: Express the result as a simplified fraction if necessary.

Now, let's work through each step:
Step 1: Both fractions are $\frac{1}{8}$ and $\frac{6}{8}$, with a common denominator of 8.
Step 2: Add the numerators: $1 + 6 = 7$.
Step 3: Use the common denominator to create the sum: $\frac{7}{8}$.
Step 4: The fraction $\frac{7}{8}$ is already in its simplest form, as 7 and 8 have no common factors other than 1.

Therefore, the solution to the problem is $\frac{7}{8}$.

To solve this problem, we need to add the two fractions with the same denominator.

• Step 1: Identify the fractions: $\frac{3}{8}$ and $\frac{4}{8}$.
• Step 2: Add the numerators since they have the same denominator: $3 + 4$.
• Step 3: The result of the addition is $\frac{7}{8}$.
• Step 4: There's no need to simplify further, as $\frac{7}{8}$ is already in its simplest form.

Therefore, the solution to the problem is $\frac{7}{8}$.

To solve the problem of $\frac{5}{8} + \frac{1}{8}$, follow these steps:

• Step 1: Identify that both fractions have the same denominator: 8.
• Step 2: Since the denominators are the same, add the numerators to get a new numerator: $5 + 1 = 6$.
• Step 3: The resulting fraction is $\frac{6}{8}$.
• Step 4: Simplify the fraction if needed; $\frac{6}{8}$ simplifies to $\frac{3}{4}$, which is a reduced form.

Therefore, the solution for the fraction addition $\frac{5}{8} + \frac{1}{8}$ is $\frac{6}{8}$, which simplifies to $\frac{3}{4}$, but considering the choices given, the answer choice corresponds to $\frac{6}{8}$, which is choice 3.

To solve this problem, we will follow these steps:

• Step 1: Identify that both fractions have the same denominator.
• Step 2: Use the formula for adding fractions with like denominators.
• Step 3: Calculate the sum of the numerators and keep the denominator unchanged.

Now, let’s work through each step:
Step 1: We observe that the fractions $\frac{5}{9}$ and $\frac{4}{9}$ both have the denominator of 9.
Step 2: We'll apply the formula for adding fractions: $\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$.
Step 3: Add the numerators 5 and 4 while keeping the denominator as 9:
$\frac{5}{9} + \frac{4}{9} = \frac{5 + 4}{9} = \frac{9}{9} = 1$.

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

To solve the given problem, follow these steps:

• Step 1: Verify that both fractions have the same denominator.
  In this case, $\frac{2}{9}$ and $\frac{3}{9}$ both have a denominator of 9.
• Step 2: Add the numerators of the fractions.
  This results in $2 + 3 = 5$.
• Step 3: Keep the denominator the same.
  Thus, the sum is $\frac{5}{9}$.

Therefore, the solution to the problem is $\frac{5}{9}$.

To solve the problem of adding the fractions $\frac{1}{9}$ and $\frac{2}{9}$, we proceed with the following steps:

• Step 1: Verify that the fractions have the same denominator.
  Both fractions, $\frac{1}{9}$ and $\frac{2}{9}$, have a common denominator of 9.
• Step 2: Add the numerators.
  The numerators are 1 and 2, respectively. So, $1 + 2 = 3$.
• Step 3: Write the result over the common denominator.
  This gives us the fraction $\frac{3}{9}$.
• Step 4: Simplify the fraction if possible.
  The fraction $\frac{3}{9}$ can be simplified by dividing the numerator and the denominator by their greatest common divisor, which is 3: $\frac{3}{9} = \frac{3 \div 3}{9 \div 3} = \frac{1}{3}$

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