Addition of Fractions

Definition

Addition of fractions is the process of combining two or more fractions to form a single, equivalent fraction. This operation is essential in simplifying and working with fractional expressions, which is a fundamental concept in pre-algebra and beyond.

5 Must Know Facts For Your Next Test

1. To add fractions with common denominators, you simply add the numerators and keep the same denominator.
2. When adding fractions with different denominators, you must first find the least common denominator (LCD) before adding the numerators.
3. The LCD is the least common multiple of the denominators of the fractions being added.
4. After finding the LCD, you convert each fraction to an equivalent fraction with the LCD as the denominator.
5. Once all the fractions have the same denominator, you can add the numerators and write the sum over the common denominator.

Review Questions

• Explain the process of adding fractions with common denominators.
  • To add fractions with common denominators, you simply add the numerators and keep the same denominator. For example, to add $\frac{1}{4}$ and $\frac{3}{4}$, you would add the numerators: $\frac{1}{4} + \frac{3}{4} = \frac{4}{4} = 1$. This works because the denominators are the same, so you can directly combine the numerators.
• Describe the steps involved in adding fractions with different denominators.
  • When adding fractions with different denominators, you must first find the least common denominator (LCD) before adding the numerators. The LCD is the least common multiple of the denominators of the fractions being added. Once you have the LCD, you convert each fraction to an equivalent fraction with the LCD as the denominator. Then, you can add the numerators and write the sum over the common denominator. For example, to add $\frac{1}{3}$ and $\frac{2}{5}$, you would first find the LCD of 3 and 5, which is 15. Then, you would convert the fractions to equivalent fractions with a denominator of 15: $\frac{1}{3} = \frac{5}{15}$ and $\frac{2}{5} = \frac{6}{15}$. Finally, you would add the numerators: $\frac{5}{15} + \frac{6}{15} = \frac{11}{15}$.
• Analyze the importance of the least common denominator (LCD) when adding fractions with different denominators.
  • The least common denominator (LCD) is crucial when adding fractions with different denominators because it allows you to convert the fractions to equivalent fractions with a common denominator. This is necessary for the addition to be possible, as you cannot directly add fractions with different denominators. By finding the LCD and converting the fractions, you ensure that the denominators are the same, enabling you to add the numerators and obtain a valid, simplified result. The LCD is the foundation for adding fractions with different denominators, as it ensures the fractions are in a compatible form for the addition operation.

Related terms

Fraction: A mathematical representation of a part of a whole, expressed as a ratio of two integers, the numerator and the denominator.

Common Denominator: The least common multiple of the denominators of two or more fractions, which allows for the addition or subtraction of those fractions.

Equivalent Fractions: Fractions that represent the same value, despite having different numerators and denominators.