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

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:

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

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:

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

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 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:

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

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:

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

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 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 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 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:

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

To solve the problem $\frac{1}{2} + \frac{2}{4}$, we'll follow these steps:

• Step 1: Convert $\frac{1}{2}$ to have a denominator of 4. Multiply the numerator and the denominator by 2 to get $\frac{2}{4}$.
• Step 2: With both fractions now having a common denominator, add them: $\frac{2}{4} + \frac{2}{4}$.
• Step 3: Combine the numerators and place the sum over the common denominator: $\frac{2+2}{4} = \frac{4}{4}$.
• Step 4: Simplify the fraction $\frac{4}{4}$ to $1$.

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

To solve this problem, we need to add the fractions $\frac{3}{5}$ and $\frac{6}{10}$. Since $\frac{6}{10}$ is already expressed with the denominator of 10, we will convert $\frac{3}{5}$ to have the same denominator.

Step 1: Convert $\frac{3}{5}$ into a fraction with a denominator of 10. To do this, multiply both the numerator and the denominator by 2:

$\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}$

Step 2: Add the fractions $\frac{6}{10}$ and $\frac{6}{10}$:

$\frac{6}{10} + \frac{6}{10} = \frac{6 + 6}{10} = \frac{12}{10}$

Step 3: Simplify $\frac{12}{10}$. Both numerator and denominator can be divided by 2:

$\frac{12}{10} = \frac{12 \div 2}{10 \div 2} = \frac{6}{5}$

Thus, the sum $\frac{3}{5} + \frac{6}{10}$ simplifies to $\frac{6}{5}$.

Therefore, the correct answer is $\frac{6}{5}$ which corresponds to choice 3.

To solve this problem, we need to add the fractions $\frac{1}{2}$ and $\frac{3}{8}$.

• Step 1: Convert $\frac{1}{2}$ to a fraction with a denominator of 8. We do this by determining the equivalent fraction $\frac{1}{2} = \frac{4}{8}$. We achieve this by multiplying the numerator and denominator by 4.
• Step 2: Now, add the fractions $\frac{4}{8}$ and $\frac{3}{8}$: $\frac{4}{8} + \frac{3}{8} = \frac{4 + 3}{8} = \frac{7}{8}$ This step involves adding the numerators while keeping the common denominator.

Therefore, the sum of $\frac{1}{2}$ and $\frac{3}{8}$ is $\frac{7}{8}$.

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

• Step 1: Identify the least common denominator (LCD) of the fractions.
• Step 2: Rewrite the fractions with the common denominator.
• Step 3: Add the fractions.
• Step 4: Simplify the resulting fraction.

Let's work through these steps:

Step 1: The denominators of our fractions are 12 and 36. The least common denominator is 36. This is because 36 is the smallest number that both 12 and 36 divide into evenly.

Step 2: Rewrite $\frac{5}{12}$ with the denominator 36. To do this, find what number 12 must be multiplied by to become 36, which is 3. Thus, multiply both the numerator and the denominator of $\frac{5}{12}$ by 3:

$\frac{5}{12} = \frac{5 \times 3}{12 \times 3} = \frac{15}{36}$.

Step 3: Now add the fractions $\frac{15}{36}$ and $\frac{11}{36}$, since they have a common denominator:

$\frac{15}{36} + \frac{11}{36} = \frac{15 + 11}{36} = \frac{26}{36}$.

Step 4: Simplify $\frac{26}{36}$. The greatest common divisor (GCD) of 26 and 36 is 2. Divide both the numerator and the denominator by 2:

$\frac{26}{36} = \frac{26 \div 2}{36 \div 2} = \frac{13}{18}$.

Therefore, the sum of $\frac{5}{12} + \frac{11}{36}$ is $\frac{13}{18}$.

The correct choice that matches this solution is choice 4.

To solve this problem, we will first convert $\frac{2}{9}$ to have a denominator of 18, then proceed to add the fractions.

Step 1: Convert $\frac{2}{9}$ to have a denominator of 18.
To convert $\frac{2}{9}$ to a fraction with a denominator of 18, recognize that 18 is twice 9. Therefore, multiply both the numerator and the denominator by 2:
$\frac{2}{9} = \frac{2 \times 2}{9 \times 2} = \frac{4}{18}$.

Step 2: Add the fractions $\frac{4}{18}$ and $\frac{3}{18}$.
Since the fractions now have the same denominator, simply add the numerators:
$\frac{4}{18} + \frac{3}{18} = \frac{4 + 3}{18} = \frac{7}{18}$.

There is no need to simplify further as $\frac{7}{18}$ is already in its simplest form.

The correct answer choice is $\frac{7}{18}$, which matches choice 1.

Therefore, the sum of $\frac{2}{9}$ and $\frac{3}{18}$ is $\frac{7}{18}$.

To solve this problem, we need to add the fractions $\frac{1}{18}$ and $\frac{1}{6}$:

Step 1: Find the least common denominator
The denominators are 18 and 6. The least common multiple of 18 and 6 is 18.

Step 2: Convert each fraction to have the least common denominator
The fraction $\frac{1}{18}$ already has the denominator 18, so it remains $\frac{1}{18}$.
To convert $\frac{1}{6}$ to a fraction with denominator 18, multiply both the numerator and denominator by 3: $\frac{1 \times 3}{6 \times 3} = \frac{3}{18}$.

Step 3: Add the converted fractions
Now that both fractions have the same denominator, add them:
$\frac{1}{18} + \frac{3}{18} = \frac{1 + 3}{18} = \frac{4}{18}$.

Step 4: Simplify the resulting fraction
$\frac{4}{18}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
$\frac{4 \div 2}{18 \div 2} = \frac{2}{9}$.

Therefore, the sum of $\frac{1}{18}$ and $\frac{1}{6}$ is $\frac{2}{9}$.

To solve the problem of adding $\frac{2}{3}$ and $\frac{1}{9}$, we follow these steps:

• Step 1: Find a common denominator.
  The denominators are 3 and 9. Since 9 is a multiple of 3, we can use 9 as the common denominator.
• Step 2: Convert the fractions to have the common denominator.
  - To convert $\frac{2}{3}$ to have a denominator of 9, multiply both the numerator and denominator by 3: $\frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}$
• Step 3: Add the fractions $\frac{6}{9}$ and $\frac{1}{9}$.
  $\frac{6}{9} + \frac{1}{9} = \frac{6+1}{9} = \frac{7}{9}$
• Step 4: Simplify the result, if necessary.
  The fraction $\frac{7}{9}$ is already in its simplest form.

Therefore, the solution to $\frac{2}{3} + \frac{1}{9}$ is $\frac{7}{9}$.

To solve $\frac{3}{4} + \frac{2}{20}$, let's follow these steps:

• Step 1: Convert $\frac{3}{4}$ to a fraction with the denominator $20$.
  Multiply both the numerator and denominator of $\frac{3}{4}$ by $5$, as $20 \div 4 = 5$:
  We have: $\frac{3 \times 5}{4 \times 5} = \frac{15}{20}$
• Step 2: The fraction $\frac{2}{20}$ is already in the correct form with a denominator of $20$.
• Step 3: Add the fractions $\frac{15}{20}$ and $\frac{2}{20}$:
  Since they have the same denominator, we combine the numerators directly: $\frac{15}{20} + \frac{2}{20} = \frac{15 + 2}{20} = \frac{17}{20}$

Therefore, the sum of the fractions is $\frac{17}{20}$.

To solve the problem of adding $\frac{3}{8}$ and $\frac{1}{4}$, we'll follow these steps:

• Step 1: Determine the Least Common Denominator (LCD).
• Step 2: Convert fractions to the common denominator.
• Step 3: Add the fractions.

Let's work through each step:
Step 1: The denominators are 8 and 4. The LCD of 8 and 4 is 8, as 8 is the smallest number that both 8 and 4 divide into without a remainder.

Step 2: Convert each fraction to have the common denominator 8.
- The fraction $\frac{3}{8}$ already has the denominator 8.
- Convert $\frac{1}{4}$ to a fraction with denominator 8: $\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}$.

Step 3: Add the fractions $\frac{3}{8}$ and $\frac{2}{8}$:
The sum is $\frac{3 + 2}{8} = \frac{5}{8}$.

Therefore, the solution to the problem is $\frac{5}{8}$.

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

• Step 1: Determine the least common denominator (LCD) of the fractions.

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

• Step 3: Add the numerators and keep the denominator the same.

Now, let's work through each step:

Step 1: The least common denominator of 15 and 5 is 15.

Step 2: Convert the fraction $\frac{2}{5}$ to have the denominator of 15.
To convert $\frac{2}{5}$, we need to multiply both the numerator and the denominator by 3, because ${5 \times 3 = 15}$.
Thus, $\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}$.

Step 3: Now, add the fractions $\frac{1}{15}$ and $\frac{6}{15}$.
When adding these fractions, the equation is $\frac{1}{15} + \frac{6}{15} = \frac{1 + 6}{15} = \frac{7}{15}$.

Therefore, the solution to the problem is $\frac{7}{15}$.

To solve the problem of adding $\frac{4}{15} + \frac{2}{5}$, follow these steps:

• Step 1: Identify a common denominator. Since 5 is a factor of 15, we will use 15 as the common denominator.
• Step 2: Convert $\frac{2}{5}$ to a fraction with a denominator of 15. To do this, multiply both the numerator and denominator by 3: $\frac{2 \times 3}{5 \times 3} = \frac{6}{15}$.
• Step 3: Add the fractions: $\frac{4}{15} + \frac{6}{15}$.
• Step 4: Since both fractions now have the same denominator, add the numerators: $\frac{4 + 6}{15} = \frac{10}{15}$.
• Step 5: Simplify $\frac{10}{15}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 5: $\frac{10 \div 5}{15 \div 5} = \frac{2}{3}$.

Therefore, the sum of $\frac{4}{15} + \frac{2}{5}$ is $\frac{2}{3}$.