## How many fractions?

#### Step-by-step solution:

With this calculator, you can add two or more fractions. You can perform operations with up to four fractions. In addition to adding fractions, you can also use the subtraction sign on some fractions.

The following instructions show how to use the calculator to add fractions. In addition, you will also find general information on how to add fractions.

## How to use the calculator to add fractions?

Step 1: Select the number of fractions you want to add. Click on “2”, “3” or “4”, as appropriate.

Step 2: Enter the fractions in the corresponding input boxes.

Step 3: Change the signs from plus to minus if necessary.

Step 5: The answer and step-by-step solution will be displayed at the bottom of the calculator.

## How to add homogeneous fractions?

Homogeneous fractions are two or more fractions that have the same denominators. To add these types of fractions, we simply have to write the fractions with a single denominator and add the numerators.

#### Example 1:

What is the result of $latex \frac{2}{5}+\frac{1}{5}$?

Solution: This is a sum of homogeneous fractions since both fractions have the same denominator. Therefore, we have to use a single denominator and add the numerators:

$$\frac{2}{5}+\frac{1}{5}$$

$$=\frac{2+1}{5}$$

$$=\frac{3}{5}$$

#### Example 2:

Find the result of $latex \frac{1}{6}+\frac{2}{6}+\frac{3}{6}$.

Solution: In this case, we have a sum of three homogeneous fractions. To solve the addition, we simply combine the denominators and add the numerators:

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

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

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

## How to add heterogeneous fractions?

Heterogeneous fractions are two or more fractions that have different denominators. We can add these types of fractions by finding the lowest common denominator (LCD).

Then, we multiply both the numerator and denominator of each fraction by a number, so that the denominator equals the least common denominator.

Once we have the fractions with the same denominator (the LCD), we can easily add them by combining the denominators and adding the numerators.

#### Example 1:

What is the result of $latex \frac{2}{3}+\frac{1}{2}$?

Solution: This is an addition of heterogeneous fractions since the fractions do not have the same denominator. Therefore, we start by finding the GCD.

In this case, the GCD of 3 and 2 equals 6. Therefore, we divide 6 by each denominator and multiply both the numerator and numerator by that number:

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

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

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

Now, we have homogeneous fractions, so we can easily add them:

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

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

$$=\frac{7}{6}$$

#### Example 2:

Find the result of the addition $latex \frac{2}{3}+\frac{3}{2}+\frac{1}{4}$.

Solution: Here, we have three heterogeneous fractions. To add these fractions, we have to start by finding the least common denominator.

In this case, the GCD of 3, 2, and 4 equals 12. Therefore, we divide 12 by each denominator and multiply both the numerator and numerator by that number:

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

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

$$=\frac{8}{12}+\frac{18}{12}+\frac{3}{12}$$

Now, we can add the like fractions easily:

$$\frac{8}{12}+\frac{18}{12}+\frac{3}{12}$$

$$=\frac{8+18+3}{12}$$

$$=\frac{29}{12}$$

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