Divide by a Number that Represents 1

Oct 13, 2025 by miodeya.com 128 views

Introduction

In mathematics, fractions are a way to represent a part of a whole. They are used to show the relationship between two numbers, where one number is a part of the other. When we have a fraction, we can simplify it to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this article, we will learn how to divide by a number that represents 1 to find the equivalent fraction in lower terms.

What is a Fraction?

A fraction is a way to represent a part of a whole. It consists of two numbers: a numerator and a denominator. The numerator is the number on top, and the denominator is the number on the bottom. For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator.

Why Do We Need to Simplify Fractions?

Simplifying fractions is important because it helps us to:

Reduce complexity: Simplifying fractions makes them easier to work with and understand.
Avoid errors: Simplifying fractions helps to avoid errors in calculations.
Make comparisons: Simplifying fractions makes it easier to compare different fractions.

How to Simplify Fractions

To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder. Once we have found the GCD, we can divide both the numerator and the denominator by the GCD to simplify the fraction.

Divide by a Number that Represents 1

A number that represents 1 is a number that is equal to 1. In other words, it is a number that does not change the value of the fraction. When we divide a fraction by a number that represents 1, we are essentially simplifying the fraction.

Example 1: Simplify the Fraction 20/30

To simplify the fraction 20/30, we need to find the greatest common divisor (GCD) of 20 and 30. The GCD of 20 and 30 is 10. We can divide both the numerator and the denominator by 10 to simplify the fraction.

\frac{20}{30} = \frac{20 ÷ 10}{30 ÷ 10} = \frac{2}{3}

Example 2: Simplify the Fraction 12/54

To simplify the fraction 12/54, we need to find the greatest common divisor (GCD) of 12 and 54. The GCD of 12 and 54 is 6. We can divide both the numerator and the denominator by 6 to simplify the fraction.

\frac{12}{54} = \frac{12 ÷ 6}{54 ÷ 6} = \frac{2}{9}

Example 3: Simplify the Fraction 16/42

To simplify the fraction 16/42, we need to find the greatest common divisor (GCD) of 16 and 42. The GCD of 16 and 42 is 2. We can divide both the numerator and the denominator by 2 to simplify the fraction.

\frac{16}{42} = \frac{16 ÷ 2}{42 ÷ 2} = \frac{8}{21}

Conclusion

In conclusion, dividing by a number that represents 1 is a way to simplify fractions. It helps us to reduce complexity, avoid errors, and make comparisons. By finding the greatest common divisor (GCD) of the numerator and the denominator, we can divide both numbers by the GCD to simplify the fraction. In this article, we have learned how to simplify three different fractions using this method.

Problem 1: Simplify the Fraction 24/36

To simplify the fraction 24/36, we need to find the greatest common divisor (GCD) of 24 and 36. The GCD of 24 and 36 is 12. We can divide both the numerator and the denominator by 12 to simplify the fraction.

\frac{24}{36} = \frac{24 ÷ 12}{36 ÷ 12} = \frac{2}{3}

Problem 2: Simplify the Fraction 18/54

To simplify the fraction 18/54, we need to find the greatest common divisor (GCD) of 18 and 54. The GCD of 18 and 54 is 18. We can divide both the numerator and the denominator by 18 to simplify the fraction.

\frac{18}{54} = \frac{18 ÷ 18}{54 ÷ 18} = \frac{1}{3}

Problem 3: Simplify the Fraction 30/60

To simplify the fraction 30/60, we need to find the greatest common divisor (GCD) of 30 and 60. The GCD of 30 and 60 is 30. We can divide both the numerator and the denominator by 30 to simplify the fraction.

\frac{30}{60} = \frac{30 ÷ 30}{60 ÷ 30} = \frac{1}{2}

Simplifying fractions is important because it helps us to reduce complexity, avoid errors, and make comparisons.
Dividing by a number that represents 1 is a way to simplify fractions.
Finding the greatest common divisor (GCD) of the numerator and the denominator is the first step in simplifying a fraction.
Dividing both the numerator and the denominator by the GCD is the second step in simplifying a fraction.

Q: What is the purpose of simplifying fractions?

A: The purpose of simplifying fractions is to reduce complexity, avoid errors, and make comparisons. Simplifying fractions makes them easier to work with and understand.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator. Once you have found the GCD, you can divide both the numerator and the denominator by the GCD to simplify the fraction.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator without leaving a remainder.

Q: How do I find the greatest common divisor (GCD)?

A: There are several ways to find the greatest common divisor (GCD). You can use the following methods:

List the factors: List the factors of the numerator and the denominator and find the greatest common factor.
Use the Euclidean algorithm: Use the Euclidean algorithm to find the greatest common divisor (GCD).
Use a calculator: Use a calculator to find the greatest common divisor (GCD).

Q: What is a number that represents 1?

A: A number that represents 1 is a number that is equal to 1. In other words, it is a number that does not change the value of the fraction.

Q: How do I divide a fraction by a number that represents 1?

A: To divide a fraction by a number that represents 1, you can simply divide the numerator and the denominator by the number that represents 1.

Q: What are some examples of simplifying fractions?

A: Here are some examples of simplifying fractions:

Simplify the fraction 20/30: To simplify the fraction 20/30, you need to find the greatest common divisor (GCD) of 20 and 30. The GCD of 20 and 30 is 10. You can divide both the numerator and the denominator by 10 to simplify the fraction.
Simplify the fraction 12/54: To simplify the fraction 12/54, you need to find the greatest common divisor (GCD) of 12 and 54. The GCD of 12 and 54 is 6. You can divide both the numerator and the denominator by 6 to simplify the fraction.
Simplify the fraction 16/42: To simplify the fraction 16/42, you need to find the greatest common divisor (GCD) of 16 and 42. The GCD of 16 and 42 is 2. You can divide both the numerator and the denominator by 2 to simplify the fraction.

Q: What are some common mistakes to avoid when simplifying fractions?

A: Here are some common mistakes to avoid when simplifying fractions:

Not finding the greatest common divisor (GCD): Make sure to find the greatest common divisor (GCD) of the numerator and the denominator before simplifying the fraction.
Not dividing both the numerator and the denominator by the GCD: Make sure to divide both the numerator and the denominator by the GCD to simplify the fraction.
Not checking for errors: Make sure to check your work for errors before simplifying the fraction.

Q: How do I practice simplifying fractions?

A: Here are some ways to practice simplifying fractions:

Use online resources: Use online resources such as Khan Academy or Mathway to practice simplifying fractions.
Use worksheets: Use worksheets to practice simplifying fractions.
Practice with real-world examples: Practice simplifying fractions with real-world examples.

Q: What are some real-world applications of simplifying fractions?

A: Here are some real-world applications of simplifying fractions:

Cooking: Simplifying fractions is useful in cooking when you need to measure ingredients.
Building: Simplifying fractions is useful in building when you need to measure materials.
Science: Simplifying fractions is useful in science when you need to measure quantities.

Q: How do I know if I have simplified a fraction correctly?

A: Here are some ways to know if you have simplified a fraction correctly:

Check your work: Make sure to check your work for errors before simplifying the fraction.
Use a calculator: Use a calculator to check your work.
Get help from a teacher or tutor: Get help from a teacher or tutor if you are unsure about simplifying a fraction.