Addition of Fractions Practice Problems with Solutions

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 $\frac{2}{7}$ 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 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 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 $\frac{1}{3}$.

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 $\frac{3}{5}$.