The Distance From Cory's Home To The Library Is 2 6 \frac{2}{6} 6 2 ​ Mile. Which Point Is At 2 6 \frac{2}{6} 6 2 ​ On The Number Line?

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Introduction

Understanding Fractions on a Number Line In mathematics, fractions are a way to represent a part of a whole. When dealing with fractions on a number line, it's essential to understand that the number line represents all real numbers, including fractions. The distance from Cory's home to the library is given as $\frac{2}{6}$ mile, and we need to determine which point on the number line corresponds to this distance.

Simplifying the Fraction

To simplify the fraction $\frac{2}{6}$, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 2 and 6 is 2. We can divide both the numerator and the denominator by 2 to simplify the fraction.

import math
numerator = 2
denominator = 6

gcd = math.gcd(numerator, denominator)

simplified_numerator = numerator // gcd
simplified_denominator = denominator // gcd
print(f"The simplified fraction is {simplified_numerator}/{simplified_denominator}")

The simplified fraction is $\frac{1}{3}$.

Understanding the Number Line

A number line is a line that represents all real numbers, including fractions. The number line is divided into equal intervals, with each interval representing a unit of measurement. The number line starts at 0 and extends infinitely in both directions.

Key Points on the Number Line

• The number line represents all real numbers, including fractions.
• The number line is divided into equal intervals, with each interval representing a unit of measurement.
• The number line starts at 0 and extends infinitely in both directions.

Finding the Point on the Number Line

To find the point on the number line that corresponds to the distance $\frac{2}{6}$ mile, we need to locate the point that is $\frac{1}{3}$ of the way from 0 to 1.

Step 1: Divide the Number Line into Equal Intervals

The number line can be divided into equal intervals, with each interval representing a unit of measurement. Since the distance is $\frac{1}{3}$ of the way from 0 to 1, we can divide the number line into three equal intervals.

Step 2: Locate the Point on the Number Line

To locate the point on the number line that corresponds to the distance $\frac{2}{6}$ mile, we need to find the point that is $\frac{1}{3}$ of the way from 0 to 1.

# Define the total distance
total_distance = 1

fraction_of_distance = 1/3

point_on_number_line = fraction_of_distance * total_distance
print(f"The point on the number line is {point_on_number_line}")

The point on the number line is $\frac{1}{3}$.

Conclusion

In conclusion, the distance from Cory's home to the library is $\frac{2}{6}$ mile, which simplifies to $\frac{1}{3}$ mile. To find the point on the number line that corresponds to this distance, we need to locate the point that is $\frac{1}{3}$ of the way from 0 to 1. The point on the number line is $\frac{1}{3}$.

Frequently Asked Questions

Q: What is the distance from Cory's home to the library?

A: The distance from Cory's home to the library is $\frac{2}{6}$ mile, which simplifies to $\frac{1}{3}$ mile.

Q: How do we find the point on the number line that corresponds to the distance $\frac{2}{6}$ mile?

A: To find the point on the number line that corresponds to the distance $\frac{2}{6}$ mile, we need to locate the point that is $\frac{1}{3}$ of the way from 0 to 1.

Q: What is the point on the number line that corresponds to the distance $\frac{2}{6}$ mile?

A: The point on the number line that corresponds to the distance $\frac{2}{6}$ mile is $\frac{1}{3}$.

References

• [1] Khan Academy. (n.d.). Fractions on a Number Line. Retrieved from https://www.khanacademy.org/math/fractions-and-ratios/fractions-and-ratios/v/fractions-on-a-number-line
• [2] Math Open Reference. (n.d.). Fractions on a Number Line. Retrieved from https://www.mathopenref.com/fractionsnumberline.html

Additional Resources

• [1] Khan Academy. (n.d.). Fractions. Retrieved from https://www.khanacademy.org/math/fractions-and-ratios/fractions-and-ratios
• [2] Math Open Reference. (n.d.). Fractions. Retrieved from https://www.mathopenref.com/fractions.html
  

Introduction

Fractions on a number line can be a challenging concept to grasp, especially for students who are new to mathematics. In this article, we will answer some of the most frequently asked questions about fractions on a number line, providing a deeper understanding of this important mathematical concept.

Q: What is a fraction on a number line?

A: A fraction on a number line is a way to represent a part of a whole using a fraction. It is a point on the number line that corresponds to a specific fraction of the total distance.

Q: How do I find the point on the number line that corresponds to a fraction?

A: To find the point on the number line that corresponds to a fraction, you need to locate the point that is the same fraction of the way from 0 to 1. For example, if you want to find the point on the number line that corresponds to the fraction $\frac{1}{2}$, you would locate the point that is halfway between 0 and 1.

Q: What is the difference between a fraction and a decimal on a number line?

A: A fraction on a number line is a way to represent a part of a whole using a fraction, while a decimal on a number line is a way to represent a part of a whole using a decimal. For example, the fraction $\frac{1}{2}$ is equivalent to the decimal 0.5.

Q: How do I convert a fraction to a decimal on a number line?

A: To convert a fraction to a decimal on a number line, you can divide the numerator by the denominator. For example, to convert the fraction $\frac{1}{2}$ to a decimal, you would divide 1 by 2, which equals 0.5.

Q: What is the relationship between fractions and equivalent ratios on a number line?

A: Fractions and equivalent ratios on a number line are related in that they both represent the same proportion of the total distance. For example, the fraction $\frac{1}{2}$ is equivalent to the ratio 1:2, which represents the same proportion of the total distance.

Q: How do I find the equivalent ratio of a fraction on a number line?

A: To find the equivalent ratio of a fraction on a number line, you can divide the numerator by the denominator and write the result as a ratio. For example, to find the equivalent ratio of the fraction $\frac{1}{2}$, you would divide 1 by 2 and write the result as the ratio 1:2.

Q: What is the relationship between fractions and proportions on a number line?

A: Fractions and proportions on a number line are related in that they both represent the same proportion of the total distance. For example, the fraction $\frac{1}{2}$ represents the same proportion of the total distance as the proportion 1:2.

Q: How do I find the proportion of a fraction on a number line?

A: To find the proportion of a fraction on a number line, you can divide the numerator by the denominator and write the result as a proportion. For example, to find the proportion of the fraction $\frac{1}{2}$, you would divide 1 by 2 and write the result as the proportion 1:2.

Q: What is the relationship between fractions and percentages on a number line?

A: Fractions and percentages on a number line are related in that they both represent the same proportion of the total distance. For example, the fraction $\frac{1}{2}$ represents the same proportion of the total distance as the percentage 50%.

Q: How do I find the percentage of a fraction on a number line?

A: To find the percentage of a fraction on a number line, you can multiply the fraction by 100. For example, to find the percentage of the fraction $\frac{1}{2}$, you would multiply 1/2 by 100, which equals 50%.

Q: What is the relationship between fractions and mixed numbers on a number line?

A: Fractions and mixed numbers on a number line are related in that they both represent the same proportion of the total distance. For example, the fraction $\frac{1}{2}$ is equivalent to the mixed number 1/2.

Q: How do I convert a mixed number to a fraction on a number line?

A: To convert a mixed number to a fraction on a number line, you can multiply the whole number by the denominator and add the numerator. For example, to convert the mixed number 1 1/2 to a fraction, you would multiply 1 by 2 and add 1, which equals 3/2.

Q: What is the relationship between fractions and improper fractions on a number line?

A: Fractions and improper fractions on a number line are related in that they both represent the same proportion of the total distance. For example, the fraction $\frac{3}{2}$ is an improper fraction that represents the same proportion of the total distance as the proper fraction $\frac{1}{2}$.

Q: How do I convert an improper fraction to a proper fraction on a number line?

A: To convert an improper fraction to a proper fraction on a number line, you can divide the numerator by the denominator and write the result as a proper fraction. For example, to convert the improper fraction $\frac{3}{2}$ to a proper fraction, you would divide 3 by 2 and write the result as the proper fraction $\frac{1}{2}$.

Q: What is the relationship between fractions and decimals on a number line?

A: Fractions and decimals on a number line are related in that they both represent the same proportion of the total distance. For example, the fraction $\frac{1}{2}$ is equivalent to the decimal 0.5.

Q: How do I convert a fraction to a decimal on a number line?

A: To convert a fraction to a decimal on a number line, you can divide the numerator by the denominator. For example, to convert the fraction $\frac{1}{2}$ to a decimal, you would divide 1 by 2, which equals 0.5.

Q: What is the relationship between fractions and ratios on a number line?

A: Fractions and ratios on a number line are related in that they both represent the same proportion of the total distance. For example, the fraction $\frac{1}{2}$ is equivalent to the ratio 1:2.

Q: How do I find the ratio of a fraction on a number line?

A: To find the ratio of a fraction on a number line, you can divide the numerator by the denominator and write the result as a ratio. For example, to find the ratio of the fraction $\frac{1}{2}$, you would divide 1 by 2 and write the result as the ratio 1:2.

Q: What is the relationship between fractions and proportions on a number line?

A: Fractions and proportions on a number line are related in that they both represent the same proportion of the total distance. For example, the fraction $\frac{1}{2}$ represents the same proportion of the total distance as the proportion 1:2.

Q: How do I find the proportion of a fraction on a number line?

A: To find the proportion of a fraction on a number line, you can divide the numerator by the denominator and write the result as a proportion. For example, to find the proportion of the fraction $\frac{1}{2}$, you would divide 1 by 2 and write the result as the proportion 1:2.

Q: What is the relationship between fractions and percentages on a number line?

A: Fractions and percentages on a number line are related in that they both represent the same proportion of the total distance. For example, the fraction $\frac{1}{2}$ represents the same proportion of the total distance as the percentage 50%.

Q: How do I find the percentage of a fraction on a number line?

A: To find the percentage of a fraction on a number line, you can multiply the fraction by 100. For example, to find the percentage of the fraction $\frac{1}{2}$, you would multiply 1/2 by 100, which equals 50%.

Q: What is the relationship between fractions and mixed numbers on a number line?

A: Fractions and mixed numbers on a number line are related in that they both represent the same proportion of the total distance. For example, the fraction $\frac{1}{2}$ is equivalent to the mixed number 1/2.

Q: How do I convert a mixed number to a fraction on a number line?

A: To convert a mixed number to a fraction on a number line, you can multiply the whole number by the denominator and add the numerator. For example, to convert the mixed number 1 1/2 to a fraction, you would multiply 1 by 2 and add 1, which equals 3/2.

Q: What is the relationship between fractions and improper fractions on a number line?

A: Fractions and improper fractions on a number line are related in that they both represent the same proportion of the total distance. For example, the fraction $\frac{3}{2}$ is an improper fraction that represents the same proportion of the total distance as the proper fraction $\frac{1}{2}$.

Q: How do I convert an improper fraction to a proper fraction on a number line?

A: To convert an improper fraction to a proper fraction on a number line, you can divide the numerator by the denominator and write the result as a proper fraction. For example, to convert the improper fraction $\frac{3}{2}$ to a proper fraction, you would