Addition of Fractions: One of the denominators is the common denominator in visual display

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

• Step 1: Identify the least common denominator of the fractions.
• Step 2: Convert each fraction to have this common denominator.
• Step 3: Add the converted fractions.

Now, let's work through each step:
Step 1: The least common denominator of 5 and 10 is 10.
Step 2: Convert $\frac{1}{5}$ to a fraction with a denominator of 10. To do this, multiply both the numerator and denominator by 2:
$\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}$
Step 3: Add the converted fraction $\frac{2}{10}$ to $\frac{7}{10}$:
$\frac{2}{10} + \frac{7}{10} = \frac{2 + 7}{10} = \frac{9}{10}$

Therefore, the solution to the problem is $\frac{9}{10}$.

To solve this problem, we need to add the fractions $\frac{2}{3}$ and $\frac{2}{9}$.

Step 1: Find a common denominator.

Given fractions have denominators 3 and 9. The least common multiple of 3 and 9 is 9. Therefore, we use 9 as the common denominator.

Step 2: Convert fractions to have the same denominator.

The second fraction, $\frac{2}{9}$, already has 9 as its denominator. We need to convert $\frac{2}{3}$ to have a denominator of 9.

To convert $\frac{2}{3}$:
Multiply both the numerator and the denominator by 3:
$\frac{2}{3} \times \frac{3}{3} = \frac{6}{9}$.

Step 3: Add the fractions $\frac{6}{9}$ and $\frac{2}{9}$.

Since the denominators are the same, add the numerators:
$\frac{6}{9} + \frac{2}{9} = \frac{6+2}{9} = \frac{8}{9}$.

Therefore, the sum of $\frac{2}{3}$ and $\frac{2}{9}$ is $\frac{8}{9}$, which corresponds to choice number 3.

To solve the problem of adding $\frac{2}{4}$ and $\frac{3}{8}$, we need to follow these steps:

• Step 1: Convert $\frac{2}{4}$ to an equivalent fraction with a denominator of 8.
• Step 2: Add the two fractions with the common denominator.
• Step 3: Verify the solution and match it against the provided answer choices.

Let's perform each step:

Step 1: Convert $\frac{2}{4}$ to a fraction with a denominator of 8.
To do this, we multiply both the numerator and the denominator of $\frac{2}{4}$ by 2, since $4 \times 2 = 8$.
This gives us $\frac{2 \times 2}{4 \times 2} = \frac{4}{8}$.

Step 2: Add $\frac{4}{8}$ and $\frac{3}{8}$.
Since both fractions now have the same denominator, we can add the numerators directly:
$\frac{4}{8} + \frac{3}{8} = \frac{4+3}{8} = \frac{7}{8}$.

Step 3: Verify the solution.
The calculated sum of the fractions is $\frac{7}{8}$. This matches choice 1 in the given answer choices.

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

To solve this problem, let's break it down into clear, manageable steps:

• Step 1: Identify the common denominator. Here, the denominators are 5 and 10. The least common denominator (LCD) is 10.
• Step 2: Convert $\frac{1}{5}$ to an equivalent fraction with a denominator of 10. This means multiplying both the numerator and denominator by 2. Thus, $\frac{1}{5} = \frac{2}{10}$.
• Step 3: We already have $\frac{3}{10}$ with a denominator of 10, so no conversion is necessary.
• Step 4: Add the two fractions: $\frac{2}{10} + \frac{3}{10} = \frac{2 + 3}{10} = \frac{5}{10}$.
• Step 5: Verify if the fraction can be simplified. Here, $\frac{5}{10}$ is already in its simplest form equivalent to $\frac{1}{2}$, but, as part of the answer choices, it appears as $\frac{5}{10}$.

Therefore, the correct answer is $\frac{5}{10}$.

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

• Step 1: Identify the least common denominator (LCD)

The denominators given are 2 and 4. The least common multiple of these numbers is 4. Thus, the least common denominator is 4.

• Step 2: Convert each fraction to have the common denominator

We need to convert $\frac{1}{2}$ to a fraction with a denominator of 4. To do this, we multiply both the numerator and the denominator of $\frac{1}{2}$ by 2:

$\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}$

The fraction $\frac{1}{4}$ already has the denominator 4, so it remains unchanged.

• Step 3: Add the converted fractions

Now add $\frac{2}{4}$ and $\frac{1}{4}$:

$\frac{2}{4} + \frac{1}{4} = \frac{2+1}{4} = \frac{3}{4}$

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

To solve the problem of adding the fractions $\frac{1}{3}$ and $\frac{3}{6}$, we must find a common denominator:

• Step 1: Identify a common denominator. Since the denominators are 3 and 6, and 6 is a multiple of 3, we can use 6 as the common denominator.

• Step 2: Convert $\frac{1}{3}$ to a fraction with a denominator of 6. To do this, multiply both the numerator and denominator of $\frac{1}{3}$ by 2 to get: $\frac{1 \times 2}{3 \times 2} = \frac{2}{6}$.

• Step 3: Now, add the converted fraction $\frac{2}{6}$ to $\frac{3}{6}$. Since they have the same denominator, we can add the numerators: $\frac{2}{6} + \frac{3}{6} = \frac{2 + 3}{6} = \frac{5}{6}$.

The answer to the problem is therefore $\frac{5}{6}$. This result matches choice id 3: $\frac{5}{6}$.

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

• Step 1: Find a common denominator for the fractions.
• Step 2: Convert $\frac{3}{4}$ to a fraction with the new denominator.
• Step 3: Add the two fractions.
• Step 4: Simplify if necessary.

Now, let's go through the process:

Step 1: The problem is $\frac{3}{4} + \frac{1}{8}$. The least common denominator (LCD) for 4 and 8 is 8.

Step 2: Convert $\frac{3}{4}$ to a fraction with a denominator of 8. To do this, multiply both the numerator and the denominator of $\frac{3}{4}$ by 2:

$\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$.

Step 3: Now, add the two fractions with the same denominator:

$\frac{6}{8} + \frac{1}{8} = \frac{6+1}{8} = \frac{7}{8}$.

Step 4: The fraction $\frac{7}{8}$ is already in its simplest form.

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

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

• Step 1: Identify the common denominator of the fractions.

• Step 2: Convert each fraction to an equivalent fraction with this common denominator.

• Step 3: Add the fractions.

Now, let's work through each step:

Step 1: The denominators of our fractions are 2 and 6. The least common denominator (LCD) between 2 and 6 is 6.

Step 2: Convert $\frac{1}{2}$ to an equivalent fraction with a denominator of 6. To do this, multiply both the numerator and the denominator by 3:

$\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$

Since $\frac{1}{6}$ already has the common denominator of 6, it remains unchanged, $\frac{1}{6}$.

Step 3: Add the fractions:

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

Therefore, the correct answer is $\frac{4}{6}$.

Verify this matches choice 4. Thus, the correct choice is :$\frac{4}{6}$

To solve this problem, we will add the fractions by first finding a common denominator:

• Step 1: Identify that the denominators are 5 and 10. Since 10 is a multiple of 5, we choose 10 as the common denominator.
• Step 2: Convert $\frac{2}{5}$ into a fraction with a denominator of 10. Multiply both numerator and denominator by 2 to get $\frac{4}{10}$.
• Step 3: Now both fractions are over 10: $\frac{4}{10}$ and $\frac{4}{10}$.
• Step 4: Add the numerators: $4 + 4 = 8$.
• Step 5: The sum is $\frac{8}{10}$.

Therefore, the solution to the problem is $\frac{8}{10}$.

The correct answer choice is: $\frac{8}{10}$.

To solve the problem of adding the fractions $\frac{1}{2}$ and $\frac{2}{4}$, we can follow these steps:

• Step 1: Convert the fraction $\frac{1}{2}$ to have the same denominator as $\frac{2}{4}$.
• Step 2: Add the two fractions.
• Step 3: Simplify the sum, if necessary.

Now, let's execute these steps in detail:
Step 1: Convert $\frac{1}{2}$ to a fraction with a denominator of 4. To do this, multiply both the numerator and the denominator by 2. Thus, $\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}$.
Step 2: Now, add the fractions $\frac{2}{4} + \frac{2}{4}$. Since the denominators are the same, we add the numerators and keep the common denominator: $\frac{2+2}{4} = \frac{4}{4}$.
Step 3: Simplify $\frac{4}{4}$, which equals 1. However, the problem asks for the sum in fraction form, so we present it as $\frac{4}{4}$.

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

To solve $\frac{1}{3} + \frac{1}{6}$, follow these steps:

• Step 1: Identify a common denominator for the fractions.
  Since $6$ is a multiple of $3$, $6$ is the common denominator.
• Step 2: Convert $\frac{1}{3}$ to a fraction with denominator $6$.
  Multiply both the numerator and denominator of $\frac{1}{3}$ by $2$:

$\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}$

• Step 3: Add the fractions $\frac{2}{6} + \frac{1}{6}$.
• Simply add the numerators and keep the common denominator:

$\frac{2}{6} + \frac{1}{6} = \frac{2 + 1}{6} = \frac{3}{6}$

Thus, after solving the addition, we get $\frac{3}{6}$.

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

• Step 1: Identify the given fractions and their denominators.
• Step 2: Determine a common denominator.
• Step 3: Convert each fraction to have the common denominator.
• Step 4: Add the fractions' numerators together.
• Step 5: Verify the answer against the possible choices.

Now, let's work through each step:

Step 1: The given fractions are $\frac{1}{5}$ and $\frac{6}{10}$.

Step 2: The common denominator for these fractions is 10, as it is already the denominator of the second fraction.

Step 3: Convert $\frac{1}{5}$ to a fraction with a denominator of 10 by multiplying both the numerator and the denominator by 2:
$\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}$.

Step 4: Add the fractions with the common denominator:
$\frac{2}{10} + \frac{6}{10} = \frac{2 + 6}{10} = \frac{8}{10}$.

Step 5: Compare the result $\frac{8}{10}$ with the possible choices given. The correct choice is $\frac{8}{10}$, which matches choice id="2".

Therefore, the solution to the problem is $\frac{8}{10}$.