Cara Pengurangan Pecahan

>Hello Sohib EditorOnline, in this article, we will discuss the methods and techniques on how to reduce fractions or “cara pengurangan pecahan” in Bahasa Indonesia. Fractions are essential in mathematics, and they are used in many daily situations in our lives. Understanding the reduction of fractions is important to simplify them, making it easier to use them in calculations and other mathematical operations.

Understanding Fractions

Fractions represent a part of a whole or a ratio between two numbers. Fractions consist of a numerator, which is the top part, and a denominator, which is the bottom part. For example, in the fraction 3/4, the number 3 is the numerator, and the number 4 is the denominator. The numerator represents how many parts we have while the denominator represents the total number of parts that make up the whole. Fractions can be proper, improper or mixed, depending on their numerator, and denominator.

Proper Fractions

A proper fraction is a fraction where the numerator is smaller than the denominator. For example, 2/5, 3/7, and 1/3 are all proper fractions. These types of fractions represent a part of a whole that is less than one. Proper fractions can also be simplified or reduced to their lowest terms.

Improper Fractions

An improper fraction has a numerator that is greater than or equal to the denominator. For example, 7/4, 5/3 and 9/8 are all improper fractions. Improper fractions represent a part of a whole that is more than one. Improper fractions can also be simplified or converted into a mixed number.

Mixed Numbers

A mixed number is a combination of a whole number and a proper fraction. For example, 3 1/2, 5 3/4 and 2 2/3 are all mixed numbers. Mixed numbers can also be converted into improper fractions or simplified to their lowest terms.

Reducing Fractions

To reduce fractions, we need to find the greatest common divisor (GCD) of the numerator and denominator, then divide both by the GCD. The resulting fraction will be in its lowest terms or simplified form. There are several methods and techniques to find the GCD.

Method 1: Prime Factorization

One method of finding the GCD is by using prime factorization. Prime factorization involves finding the prime factors of each number and multiplying the common prime factors. For example, to reduce the fraction 12/20 to its lowest terms, we need to find the GCD of 12 and 20. Prime factorization of 12 yields 2 x 2 x 3 while prime factorization of 20 yields 2 x 2 x 5.

Number Prime Factors
12 2 x 2 x 3
20 2 x 2 x 5

The common prime factors between 12 and 20 are 2 and 2. Therefore, the GCD of 12 and 20 is 2 x 2 = 4. To reduce 12/20 to its lowest terms, we divide both numerator and denominator by 4. The resulting fraction is 3/5.

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Method 2: Euclidean Algorithm

Another method for finding the GCD of two numbers is the Euclidean algorithm. It involves dividing the larger number by the smaller number and then taking the remainder. We continue this process until we obtain a remainder of zero. The last non-zero remainder is the GCD of the two numbers.

For example, to reduce 24/36 to its lowest terms, we use the Euclidean algorithm as follows:

Number Division Remainder
36 ÷24 12
24 ÷12 0

The GCD of 24 and 36 is the last non-zero remainder, which is 12. To simplify 24/36, we divide both numerator and denominator by 12. The resulting fraction is 2/3.

Frequently Asked Questions

1. What is a fraction?

A fraction represents a part of a whole or a ratio between two numbers. Fractions consist of a numerator, which is the top part, and a denominator, which is the bottom part. The numerator represents how many parts we have while the denominator represents the total number of parts that make up the whole.

2. What is a proper fraction?

A proper fraction is a fraction where the numerator is smaller than the denominator. Proper fractions represent a part of a whole that is less than one and can be simplified or reduced to their lowest terms.

3. What is an improper fraction?

An improper fraction has a numerator that is greater than or equal to the denominator. Improper fractions represent a part of a whole that is more than one and can be converted into a mixed number or simplified to their lowest terms.

4. How do you reduce fractions?

To reduce fractions, we need to find the greatest common divisor (GCD) of the numerator and denominator, then divide both by the GCD. The resulting fraction will be in its lowest terms or simplified form. There are several methods and techniques to find the GCD, such as prime factorization and Euclidean algorithm.

5. Why is reducing fractions important?

Reducing or simplifying fractions is important because it makes them easier to use in calculations and other mathematical operations. Simplifying fractions also helps in understanding the relationship between different fractions and their equivalents.

Conclusion

In conclusion, reducing fractions or “cara pengurangan pecahan” is an essential skill in mathematics. Understanding fractions, their types and reducing them to their lowest terms is crucial in simplifying mathematical operations involving fractions. We hope that this article has provided you with the necessary information and techniques to reduce fractions easily and correctly.

Cara Pengurangan Pecahan