## How to Add and Subtract Fractions with Different Denominators

**Adding and Subtracting Fractions with Different Denominators**

Adding and subtracting fractions with different denominators might seem tricky at first, but with a clear method, it becomes straightforward. When dealing with fractions that have different denominators, the key is to find a common denominator, which is a shared multiple of the denominators of the fractions you are working with.

To add or subtract fractions, follow these steps:

**Find a Common Denominator**: This is a number that both denominators can divide into evenly. The least common denominator (LCD) is often the easiest to work with.**Convert the Fractions**: Adjust each fraction to make their denominators the same. You do this by multiplying the numerator and the denominator of each fraction by whatever number will make the denominators equal to the common denominator.**Add or Subtract the Numerators**: Once the fractions have the same denominator, you can add or subtract the numerators as required.**Simplify the Resulting Fraction**: If necessary, simplify the fraction to its lowest terms.

Let's break down these steps with a friendly example.

**Example: The Magic of Sharing Pizza**

Imagine you and your friend have two different slices of pizza, and you want to know how much pizza you have altogether. One slice is three-fifths of a pizza, and the other slice is one-third of a pizza. How much pizza do you have in total?

**Find a Common Denominator**:The denominators are 5 and 3.

The least common multiple of 5 and 3 is 15, so 15 will be our common denominator.

**Convert the Fractions**:For three-fifths, multiply both the numerator and the denominator by 3. This gives us nine-fifteenths (3 x 3 / 5 x 3).

For one-third, multiply both the numerator and the denominator by 5. This gives us five-fifteenths (1 x 5 / 3 x 5).

**Add the Fractions**:Now we have nine-fifteenths and five-fifteenths.

Adding these together, we get fourteen-fifteenths (9 + 5 / 15).

**Simplify the Fraction**:In this case, fourteen-fifteenths is already in its simplest form.

So, when you combine the two slices of pizza, you have fourteen-fifteenths of a pizza 🍕!

**Example: Subtracting for the Win**

Now, imagine you ate one-fourth of a cake, and later you ate one-sixth of another cake. How much more cake did you eat the first time compared to the second time?

**Find a Common Denominator**:The denominators are 4 and 6.

The least common multiple of 4 and 6 is 12, so 12 will be our common denominator.

**Convert the Fractions**:For one-fourth, multiply both the numerator and the denominator by 3. This gives us three-twelfths (1 x 3 / 4 x 3).

For one-sixth, multiply both the numerator and the denominator by 2. This gives us two-twelfths (1 x 2 / 6 x 2).

**Subtract the Fractions**:Now we have three-twelfths and two-twelfths.

Subtracting these, we get one-twelfth (3 - 2 / 12).

**Simplify the Fraction**:One-twelfth is already in its simplest form.

So, you ate one-twelfth more cake the first time 🎂!