Pecahan Senilai dan Operasi Hitung: Penjumlahan dan Pengurangan

The concept of equivalent fractions, or pecahan senilai in Indonesian, is a fundamental building block in mathematics, particularly in the realm of fractions. Understanding equivalent fractions is crucial for performing various operations, including addition and subtraction, with fractions. This article delves into the essence of equivalent fractions and explores how they facilitate the process of adding and subtracting fractions.

Understanding Equivalent Fractions

Equivalent fractions represent the same portion of a whole, even though they may have different numerators and denominators. The key principle behind equivalent fractions is that multiplying or dividing both the numerator and denominator of a fraction by the same non-zero number results in an equivalent fraction. For instance, 1/2, 2/4, and 3/6 are all equivalent fractions because they represent the same half of a whole. This concept is essential for simplifying fractions and finding common denominators for addition and subtraction.

Adding Fractions with Equivalent Fractions

Adding fractions with different denominators requires finding a common denominator. This is where equivalent fractions come into play. To add fractions, we need to express them with the same denominator. This is achieved by finding the least common multiple (LCM) of the denominators and converting each fraction into an equivalent fraction with the LCM as the denominator. For example, to add 1/3 and 1/4, we find the LCM of 3 and 4, which is 12. We then convert 1/3 to 4/12 and 1/4 to 3/12. Now, with the same denominator, we can add the fractions: 4/12 + 3/12 = 7/12.

Subtracting Fractions with Equivalent Fractions

Similar to addition, subtracting fractions with different denominators requires finding a common denominator. We use the same principle of equivalent fractions to achieve this. We find the LCM of the denominators and convert each fraction into an equivalent fraction with the LCM as the denominator. For example, to subtract 2/5 from 3/4, we find the LCM of 5 and 4, which is 20. We then convert 2/5 to 8/20 and 3/4 to 15/20. Now, with the same denominator, we can subtract the fractions: 15/20 - 8/20 = 7/20.

Simplifying Fractions with Equivalent Fractions

Equivalent fractions are also crucial for simplifying fractions. Simplifying a fraction means expressing it in its simplest form, where the numerator and denominator have no common factors other than 1. This is achieved by dividing both the numerator and denominator by their greatest common factor (GCD). For example, the fraction 6/8 can be simplified by dividing both the numerator and denominator by their GCD, which is 2. This results in the simplified fraction 3/4.

Conclusion

Equivalent fractions play a pivotal role in understanding and performing operations with fractions. They enable us to find common denominators for addition and subtraction, simplify fractions to their simplest form, and ultimately, solve various mathematical problems involving fractions. By mastering the concept of equivalent fractions, we gain a deeper understanding of the world of fractions and its applications in various fields.