What Is $\frac{9}{21}$ In Its Lowest Terms?
Introduction
Understanding Fractions: Fractions are a way to represent a part of a whole. They consist of a numerator (the top number) and a denominator (the bottom number). In this article, we will focus on simplifying the fraction $\frac{9}{21}$ to its lowest terms.
What are Lowest Terms?
Definition: The lowest terms of a fraction are the simplest form of the fraction, where the numerator and denominator have no common factors other than 1. In other words, the fraction is in its most reduced form.
Simplifying Fractions
Method 1: Finding Common Factors: To simplify a fraction, we need to find the greatest common factor (GCF) of the numerator and denominator. The GCF is the largest number that divides both numbers without leaving a remainder.
Example: Simplifying $\frac{9}{21}$
To simplify $\frac{9}{21}$, we need to find the GCF of 9 and 21. The factors of 9 are 1, 3, and 9. The factors of 21 are 1, 3, 7, and 21. The greatest common factor of 9 and 21 is 3.
Step 1: Divide the Numerator and Denominator by the GCF
We will divide both the numerator and denominator by the GCF (3).
Step 2: Check if the Fraction is in its Lowest Terms
We need to check if the fraction $\frac{3}{7}$ is in its lowest terms. To do this, we need to find the GCF of 3 and 7. The factors of 3 are 1 and 3. The factors of 7 are 1 and 7. The greatest common factor of 3 and 7 is 1.
Since the GCF of 3 and 7 is 1, the fraction $\frac{3}{7}$ is in its lowest terms.
Conclusion
In this article, we simplified the fraction $\frac{9}{21}$ to its lowest terms. We found the GCF of 9 and 21, which is 3. We then divided both the numerator and denominator by the GCF to get the simplified fraction $\frac{3}{7}$. We checked if the fraction is in its lowest terms by finding the GCF of 3 and 7, which is 1. Since the GCF of 3 and 7 is 1, the fraction $\frac{3}{7}$ is in its lowest terms.
Frequently Asked Questions
Q: What is the lowest terms of a fraction?
A: The lowest terms of a fraction are the simplest form of the fraction, where the numerator and denominator have no common factors other than 1.
Q: How do I simplify a fraction?
A: To simplify a fraction, you need to find the greatest common factor (GCF) of the numerator and denominator. You then divide both the numerator and denominator by the GCF to get the simplified fraction.
Q: What is the greatest common factor (GCF)?
A: The greatest common factor (GCF) is the largest number that divides both numbers without leaving a remainder.
Example Problems
Problem 1: Simplify $\frac{12}{18}$
To simplify $\frac{12}{18}$, we need to find the GCF of 12 and 18. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The greatest common factor of 12 and 18 is 6.
We will divide both the numerator and denominator by the GCF (6).
Problem 2: Simplify $\frac{15}{25}$
To simplify $\frac{15}{25}$, we need to find the GCF of 15 and 25. The factors of 15 are 1, 3, 5, and 15. The factors of 25 are 1, 5, and 25. The greatest common factor of 15 and 25 is 5.
We will divide both the numerator and denominator by the GCF (5).
Practice Problems
Problem 1: Simplify $\frac{18}{24}$
To simplify $\frac{18}{24}$, we need to find the GCF of 18 and 24. The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The greatest common factor of 18 and 24 is 6.
We will divide both the numerator and denominator by the GCF (6).
Problem 2: Simplify $\frac{20}{30}$
To simplify $\frac{20}{30}$, we need to find the GCF of 20 and 30. The factors of 20 are 1, 2, 4, 5, 10, and 20. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The greatest common factor of 20 and 30 is 10.
We will divide both the numerator and denominator by the GCF (10).
Conclusion
In this article, we simplified the fraction $\frac{9}{21}$ to its lowest terms. We found the GCF of 9 and 21, which is 3. We then divided both the numerator and denominator by the GCF to get the simplified fraction $\frac{3}{7}$. We checked if the fraction is in its lowest terms by finding the GCF of 3 and 7, which is 1. Since the GCF of 3 and 7 is 1, the fraction $\frac{3}{7}$ is in its lowest terms.
We also provided example problems and practice problems to help you understand how to simplify fractions. We hope this article has been helpful in understanding the concept of simplifying fractions.
Introduction
Simplifying fractions is an essential concept in mathematics that helps us to reduce complex fractions to their simplest form. In this article, we will answer some of the most frequently asked questions about simplifying fractions.
Q: What is the greatest common factor (GCF)?
A: The greatest common factor (GCF) is the largest number that divides both numbers without leaving a remainder. It is used to simplify fractions by dividing both the numerator and denominator by the GCF.
Q: How do I find the GCF of two numbers?
A: To find the GCF of two numbers, you need to list the factors of each number and find the largest common factor. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The greatest common factor of 12 and 18 is 6.
Q: What is the difference between simplifying a fraction and reducing a fraction?
A: Simplifying a fraction means reducing it to its simplest form by dividing both the numerator and denominator by their greatest common factor. Reducing a fraction means finding the simplest form of the fraction by dividing both the numerator and denominator by their greatest common factor.
Q: Can a fraction be simplified if the numerator and denominator have no common factors?
A: Yes, a fraction can be simplified even if the numerator and denominator have no common factors. In this case, the fraction is already in its simplest form.
Q: How do I know if a fraction is in its simplest form?
A: To check if a fraction is in its simplest form, you need to find the greatest common factor of the numerator and denominator. If the greatest common factor is 1, then the fraction is in its simplest form.
Q: Can a fraction be simplified if the numerator and denominator have a common factor of 1?
A: Yes, a fraction can be simplified if the numerator and denominator have a common factor of 1. In this case, the fraction is already in its simplest form.
Q: What is the purpose of simplifying fractions?
A: The purpose of simplifying fractions is to reduce complex fractions to their simplest form, making it easier to perform mathematical operations such as addition, subtraction, multiplication, and division.
Q: Can a fraction be simplified if it has a negative numerator or denominator?
A: Yes, a fraction can be simplified even if it has a negative numerator or denominator. The process of simplifying a fraction remains the same, regardless of whether the numerator or denominator is negative.
Q: How do I simplify a fraction with a variable in the numerator or denominator?
A: To simplify a fraction with a variable in the numerator or denominator, you need to find the greatest common factor of the variable and the other number. Then, you can simplify the fraction by dividing both the numerator and denominator by the greatest common factor.
Q: Can a fraction be simplified if it has a decimal in the numerator or denominator?
A: Yes, a fraction can be simplified even if it has a decimal in the numerator or denominator. The process of simplifying a fraction remains the same, regardless of whether the numerator or denominator has a decimal.
Q: How do I simplify a fraction with a mixed number in the numerator or denominator?
A: To simplify a fraction with a mixed number in the numerator or denominator, you need to convert the mixed number to an improper fraction. Then, you can simplify the fraction by finding the greatest common factor of the numerator and denominator.
Q: Can a fraction be simplified if it has a fraction in the numerator or denominator?
A: Yes, a fraction can be simplified even if it has a fraction in the numerator or denominator. The process of simplifying a fraction remains the same, regardless of whether the numerator or denominator has a fraction.
Q: How do I simplify a fraction with a negative exponent in the numerator or denominator?
A: To simplify a fraction with a negative exponent in the numerator or denominator, you need to rewrite the fraction with a positive exponent. Then, you can simplify the fraction by finding the greatest common factor of the numerator and denominator.
Q: Can a fraction be simplified if it has a zero in the numerator or denominator?
A: No, a fraction cannot be simplified if it has a zero in the numerator or denominator. In this case, the fraction is undefined.
Conclusion
In this article, we have answered some of the most frequently asked questions about simplifying fractions. We hope this article has been helpful in understanding the concept of simplifying fractions and how to apply it to different types of fractions.