Addition of Fractions: One of the denominators is the common denominator

We must first identify the lowest common denominator between 3 and 6.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 3 and 6.

In this case, the common denominator is 6.

We'll then proceed to multiply each fraction by the appropriate number to reach the denominator 6.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{1\times2}{3\times2}+\frac{3\times1}{6\times1}=\frac{2}{6}+\frac{3}{6}$

Finally we'll combine and obtain the following:

$\frac{2+3}{6}=\frac{5}{6}$

Let's first identify the lowest common denominator between 2 and 8.

In order to determine the lowest common denominator, we need to first find a number that is divisible by both 2 and 8.

In this case, the common denominator is 8.

We'll then proceed to multiply each fraction by the appropriate number in order to reach the denominator 8.

We'll multiply the first fraction by 4

We'll multiply the second fraction by 1

$\frac{1\times4}{2\times4}+\frac{3\times1}{8\times1}=\frac{4}{8}+\frac{3}{8}$

Finally we'll combine and obtain the following:

$\frac{4+3}{8}=\frac{7}{8}$

To solve the problem of adding $\frac{2}{3}$ and $\frac{1}{6}$, we will first find a common denominator:

• Step 1: Identify the least common denominator (LCD), which is 6 for the fractions $\frac{2}{3}$ and $\frac{1}{6}$.
• Step 2: Convert $\frac{2}{3}$ to an equivalent fraction with a denominator of 6. To do this, multiply both the numerator and the denominator by 2: $\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$
• Step 3: Now, add the fractions $\frac{4}{6}$ and $\frac{1}{6}$: $\frac{4}{6} + \frac{1}{6} = \frac{4 + 1}{6} = \frac{5}{6}$

As we see, both fractions have been added correctly. The sum is already in its simplest form.

Therefore, the solution to the problem is $\frac{5}{6}$.

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

• Step 1: Convert $\frac{1}{4}$ to a fraction with a denominator of 8.
• Step 2: Add the fractions.
• Step 3: Simplify the result.

Now, let's work through each step:

Step 1: Convert $\frac{1}{4}$ to have a denominator of 8. Since $8 \div 4 = 2$, multiply both the numerator and denominator of $\frac{1}{4}$ by 2:

$\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}$

Step 2: Now add $\frac{2}{8}$ and $\frac{4}{8}$:

$\frac{2}{8} + \frac{4}{8} = \frac{2 + 4}{8} = \frac{6}{8}$

Step 3: Simplify $\frac{6}{8}$ if possible. The greatest common divisor of 6 and 8 is 2. So, $\frac{6}{8}$ simplifies to:

$\frac{6 \div 2}{8 \div 2} = \frac{3}{4}$

Therefore, the solution to the problem is $\frac{6}{8}$.

To solve this addition problem involving fractions, we first need to ensure both fractions have a common denominator.

Step 1: Convert $\frac{1}{4}$ to an equivalent fraction with a denominator of 8.

To do this, we need to multiply both the numerator and denominator of $\frac{1}{4}$ by 2 to achieve the desired denominator:

$\frac{1 \times 2}{4 \times 2} = \frac{2}{8}$

Step 2: Now we can add the fractions $\frac{2}{8}$ and $\frac{3}{8}$ since they have a common denominator.

$\frac{2}{8} + \frac{3}{8} = \frac{2 + 3}{8} = \frac{5}{8}$

Therefore, the sum of $\frac{1}{4}$ and $\frac{3}{8}$ is $\frac{5}{8}$.

Thus, the correct answer to the problem is $\frac{5}{8}$.

We must first identify the lowest common denominator between 4 and 8

In order to determine the lowest common denominator, we need to find a number that is divisible by both 4 and 8.

In this case, the common denominator is 8.

We will proceed to multiply each fraction by the appropriate number to reach the denominator 8.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{2\times2}{4\times2}+\frac{1\times1}{8\times1}=\frac{4}{8}+\frac{1}{8}$

Finally we'll combine and obtain the following:

$\frac{4+1}{8}=\frac{5}{8}$

Let's begin by identifying the lowest common denominator between 3 and 6.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 3 and 6.

In this case, the common denominator is 6.

Let's proceed to multiply each fraction by the appropriate number in order to reach the denominator 6.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{2\times2}{3\times2}+\frac{1\times1}{6\times1}=\frac{4}{6}+\frac{1}{6}$

Finally we'll combine and obtain the following result:

$\frac{4+1}{6}=\frac{5}{6}$

We must first identify the lowest common denominator between 5 and 10.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 5 and 10.

In this case, the common denominator is 10.

We will proceed to multiply each fraction by the appropriate number to reach the denominator 10.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{1\times2}{5\times2}+\frac{6\times1}{10\times1}=\frac{2}{10}+\frac{6}{10}$

Finally we'll combine and obtain the following:

$\frac{2+6}{10}=\frac{8}{10}$

Let's first identify the lowest common denominator between 4 and 2.

In order to identify the lowest common denominator, we need to find a number that is divisible by both 4 and 2.

In this case, the common denominator is 4

We will then proceed to multiply each fraction by the appropriate number in order to reach the denominator 4

We'll multiply the first fraction by 1

We'll multiply the second fraction by 2

$\frac{2\times1}{4\times1}+\frac{1\times2}{2\times2}=\frac{2}{4}+\frac{2}{4}$

Finally we will combine and obtain the following:

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

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

• Identify the common denominator.
• Convert each fraction to an equivalent fraction with the common denominator.
• Add the fractions.
• Verify the solution against given choices.

Now, let's work through each step:

Step 1: Identify the common denominator. For fractions $\frac{1}{3}$ and $\frac{1}{6}$, the least common multiple (LCM) of 3 and 6 is 6.

Step 2: Convert $\frac{1}{3}$ to have a denominator of 6. We do this by multiplying both the numerator and denominator by 2:

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

The fraction $\frac{1}{6}$ already has a denominator of 6, so we leave it unchanged:

$\frac{1}{6} = \frac{1}{6}$

Step 3: Add the fractions:

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

The fraction $\frac{3}{6}$ simplifies to $\frac{1}{2}$, but since the task is to match with given choices, we note that there is no need to simplify further.

After comparing with the given choices, the option that matches our calculation is:

$\frac{3}{6}$

To solve the problem of adding the fractions $\frac{1}{4}$ and $\frac{1}{8}$, follow these steps:

• Step 1: Identify the denominators: 4 and 8. We need a common denominator to add the fractions.
• Step 2: Find the least common multiple (LCM) of 4 and 8. The smallest number that both 4 and 8 can divide is 8, so our common denominator will be 8.
• Step 3: Convert $\frac{1}{4}$ to a fraction with denominator 8. To do this, multiply both the numerator and the denominator of $\frac{1}{4}$ by 2:
• $\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}$
• Step 4: Now add the fractions: $\frac{2}{8} + \frac{1}{8}$.
• Since the fractions now have the same denominator, add the numerators: $2 + 1 = 3$, while keeping the denominator 8.
• The result is $\frac{3}{8}$.
• Step 5: Ensure the fraction is in its simplest form. The fraction $\frac{3}{8}$ is already simplified, as 3 and 8 have no common factors other than 1.

Therefore, the sum of $\frac{1}{4} + \frac{1}{8}$ is $\frac{3}{8}$.

Once we compare this with the given answer choices, we find that our final result, $\frac{3}{8}$, matches choice 1.

Hence, the correct answer to the problem is $\frac{3}{8}$.

To solve the problem of adding $\frac{1}{6} + \frac{4}{12}$, follow these steps:

• Step 1: Find the least common denominator (LCD) for the fractions. The denominators are 6 and 12, and the LCD is 12.
• Step 2: Convert $\frac{1}{6}$ to an equivalent fraction with a denominator of 12. To do this, multiply both the numerator and the denominator by 2: $\frac{1}{6} \times \frac{2}{2} = \frac{2}{12}$.
• Step 3: The fraction $\frac{4}{12}$ already has the denominator of 12, so no conversion is needed.
• Step 4: Add the fractions with the common denominator: $\frac{2}{12} + \frac{4}{12} = \frac{6}{12}$.
• Step 5: Simplify the resulting fraction if possible. In this case, $\frac{6}{12}$ simplifies to $\frac{1}{2}$, but we will leave it as $\frac{6}{12}$ as it appears in the options.

Therefore, the solution to the problem is $\frac{6}{12}$, which matches option 3 from the provided answers.

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

• Step 1: Convert the fractions to have the same denominator.
• Step 2: Add the fractions.
• Step 3: Simplify the resulting fraction.

Let's proceed with solving the problem:

Step 1: Convert $\frac{2}{5}$ to a fraction with a denominator of 10. The equivalent fraction is found by multiplying the numerator and the denominator by 2:

$\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}$

Step 2: Add the fractions $\frac{4}{10}$ and $\frac{5}{10}$:

$\frac{4}{10} + \frac{5}{10} = \frac{4 + 5}{10} = \frac{9}{10}$

Step 3: Simplify the resulting fraction. Since $\frac{9}{10}$ is already in its simplest form, we conclude:

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

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

• Step 1: Identify the least common denominator (LCD) of the fractions $\frac{1}{4}$ and $\frac{1}{2}$.
• Step 2: Convert each fraction to have the common denominator.
• Step 3: Add the fractions together.

Now, let's work through each step:

Step 1: Identify the Least Common Denominator (LCD).

The denominators are 4 and 2. The smallest number that both 4 and 2 can divide into without a remainder is 4. Thus, the LCD is 4.

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

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

The fraction $\frac{1}{2}$ needs to be converted. We multiply both the numerator and denominator by 2 to get the equivalent fraction $\frac{2}{4}$.

Step 3: Add the fractions.

The fractions $\frac{1}{4}$ and $\frac{2}{4}$ share a common denominator, so we can add the numerators:

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

Therefore, the solution to the problem is $\frac{3}{4}$.

We must first identify the lowest common denominator between 3 and 9.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 3 and 9.

In this case, the common denominator is 9.

We will then proceed to multiply each fraction by the appropriate number to reach the denominator 9.

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

$\frac{1\times3}{3\times3}+\frac{4\times1}{9\times1}=\frac{3}{9}+\frac{4}{9}$

Finally we'll combine and obtain the following:

$\frac{3+4}{9}=\frac{7}{9}$

Let's try to find the lowest common denominator between 3 and 9

To find the lowest common denominator, we need to find a number that is divisible by both 3 and 9

In this case, the common denominator is 9

Now we'll multiply each fraction by the appropriate number to reach the denominator 9

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

$\frac{1\times3}{3\times3}+\frac{5\times1}{9\times1}=\frac{3}{9}+\frac{5}{9}$

Now we'll combine and get:

$\frac{3+5}{9}=\frac{8}{9}$

We must first identify the lowest common denominator between 3 and 9.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 3 and 9.

In this case, the common denominator is 9.

We will then proceed to multiply each fraction by the appropriate number to reach the denominator 9.

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

$\frac{1\times3}{3\times3}+\frac{2\times1}{9\times1}=\frac{2}{9}+\frac{2}{9}$

Finally we'll combine and obtain the following:

$\frac{2+3}{9}=\frac{5}{9}$

Let's try to find the lowest common denominator between 5 and 15

To find the lowest common denominator, we need to find a number that is divisible by both 5 and 15

In this case, the common denominator is 15

Now we'll multiply each fraction by the appropriate number to reach the denominator 15

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

$\frac{1\times3}{5\times3}+\frac{2\times1}{15\times1}=\frac{3}{15}+\frac{2}{15}$

Now we'll combine and get:

$\frac{3+2}{15}=\frac{5}{15}$

We must first identify the lowest common denominator between 4 and 12.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 4 and 12.

In this case, the common denominator is 12.

We will then proceed to multiply each fraction by the appropriate number to reach the denominator 12.

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

$\frac{1\times3}{4\times3}+\frac{6\times1}{12\times1}=\frac{3}{12}+\frac{6}{12}$

Finally we'll combine and obtain the following:

$\frac{3+6}{12}=\frac{9}{12}$

Let's try to find the lowest common denominator between 5 and 15

To find the lowest common denominator, we need to find a number that is divisible by both 5 and 15

In this case, the common denominator is 15

Now we'll multiply each fraction by the appropriate number to reach the denominator 15

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

$\frac{3\times3}{5\times3}+\frac{2\times1}{15\times1}=\frac{9}{15}+\frac{2}{15}$

Now we'll combine and get:

$\frac{9+2}{15}=\frac{11}{15}$