Adding fractions with Different Denominators

In this lesson, we will learn how to add fractions that have different denominators. This is an important skill that helps us combine parts of a whole.

Steps to Add fractions with Different Denominators

1. Find a Common Denominator: The first step is to find the least common denominator (LCD) for the fractions.
2. Convert the fractions: Convert each fraction to an equivalent fraction with the common denominator.
3. Add the Numerators: Once the fractions have the same denominator, add the numerators together.
4. Simplify the Result: If possible, simplify the resulting fraction.

Example

Let's add the fractions $\frac{1}{3}$ and $\frac{1}{4}$.

1. Find the Common Denominator: The denominators are 3 and 4. The least common multiple of 3 and 4 is 12.

2. Convert the fractions:

   • For $\frac{1}{3}$: $\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$
   • For $\frac{1}{4}$: $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$

3. Add the Numerators: $\frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12}$

4. Simplify the Result: The result $\frac{7}{12}$ is already in its simplest form.

Thus, $\frac{1}{3} + \frac{1}{4} = \frac{7}{12}$.

Key Questions

• What is a common denominator?
• How do you find the least common multiple of two numbers?
• Why is it necessary to convert fractions to the same denominator before adding them?

Keywords

• fractions
• Common Denominator
• Adding fractions
• Least Common Multiple
• Simplifying fractions