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

Let's try to find the lowest common denominator between 2 and 10

To find the lowest common denominator, we need to find a number that is divisible by both 2 and 10

In this case, the common denominator is 10

Now we'll multiply each fraction by the appropriate number to reach the denominator 10

We'll multiply the first fraction by 5

We'll multiply the second fraction by 1

$\frac{1\times5}{2\times5}+\frac{2\times1}{10\times1}=\frac{5}{10}+\frac{2}{10}$

Now we'll combine and get:

$\frac{5+2}{10}=\frac{7}{10}$

Let's try to find the least common denominator between 2 and 10

To find the least common denominator, we need to find a number that is divisible by both 2 and 10

In this case, the common denominator is 10

Now we'll multiply each fraction by the appropriate number to reach the denominator 10

We'll multiply the first fraction by 5

We'll multiply the second fraction by 1

$\frac{1\times5}{2\times5}+\frac{3\times1}{10\times1}=\frac{5}{10}+\frac{3}{10}$

Now we'll combine and get:

$\frac{5+3}{10}=\frac{8}{10}$

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:

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

Let's try to find the least common denominator between 4 and 8

To find the least common denominator, we need to find a number that is divisible by both 4 and 8

In this case, the common denominator is 8

Now we'll 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

$\frac{1\times2}{4\times2}+\frac{6\times1}{8\times1}=\frac{2}{8}+\frac{6}{8}$

Now we'll combine and get:

$\frac{2+6}{8}=\frac{8}{8}=1$

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:

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

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:

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

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:

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

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:

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

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:

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

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:

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

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:

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

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 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:

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

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:

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

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:

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

To solve this problem, we will follow these steps:

• Step 1: Identify the given fractions $\frac{1}{2}$ and $\frac{2}{8}$.
• Step 2: Determine a common denominator for both fractions. Since 8 is a multiple of 2, we will use 8 as the common denominator.
• Step 3: Convert $\frac{1}{2}$ to an equivalent fraction with a denominator of 8.
• Step 4: Add the fractions together.

Now, let's work through these steps:

Step 1: The fractions given are $\frac{1}{2}$ and $\frac{2}{8}$.

Step 2: We choose 8 as the common denominator because it is a multiple of 2.

Step 3: Convert $\frac{1}{2}$ to have a denominator of 8. To do this, multiply both the numerator and the denominator of $\frac{1}{2}$ by 4:

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

The fractions now are $\frac{4}{8}$ and $\frac{2}{8}$, both having the common denominator 8.

Step 4: Add the numerators of these fractions:

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

Therefore, the sum of $\frac{1}{2} + \frac{2}{8}$ is $\frac{6}{8}$.

To solve the problem, follow these steps:

• Step 1: Recognize the denominators $2$ and $10$ and note that $10$ is a common multiple.
• Step 2: Convert $\frac{1}{2}$ to a fraction with a denominator of 10. Since $2 \times 5 = 10$, multiply both the numerator and denominator of $\frac{1}{2}$ by 5 to get $\frac{5}{10}$.
• Step 3: The second fraction, $\frac{3}{10}$, already has a denominator of 10, so no conversion is needed.
• Step 4: Add the two fractions: $\frac{5}{10} + \frac{3}{10}$.
• Step 5: As the denominators are the same, add the numerators: $5 + 3 = 8$.
• Step 6: Write the result with the common denominator: $\frac{8}{10}$.
• Step 7: Check if the fraction can be simplified further. Since 8 and 10 have a common factor of 2, divide by 2 to simplify: $\frac{8}{10} = \frac{4}{5}$.

The problem's correct answer without simplification matches choice 1.

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

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 this problem, let's follow these steps:

• Step 1: Identify the common denominator.
  Since 9 is a multiple of 3, our least common denominator will be 9.
• Step 2: Convert $\frac{1}{3}$ to an equivalent fraction with a denominator of 9.
  To do this, multiply both the numerator and the denominator by 3: $\frac{1 \times 3}{3 \times 3} = \frac{3}{9}$.
• Step 3: The other fraction, $\frac{2}{9}$, already has the denominator 9, so we don't need to change it.
• Step 4: Add the fractions $\frac{3}{9} + \frac{2}{9}$.
• Step 5: Add the numerators: $3 + 2 = 5$.
• Step 6: Combine over the common denominator: $\frac{5}{9}$.

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

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 $\frac{3}{4}$.