Which Fraction Is Greater Than 33 8 \frac{33}{8} 8 33 ​ ?A. 19 6 \frac{19}{6} 6 19 ​ B. 13 3 \frac{13}{3} 3 13 ​ C. 26 9 \frac{26}{9} 9 26 ​ D. 47 12 \frac{47}{12} 12 47 ​

Introduction

Comparing fractions is an essential skill in mathematics, and it's often used in various real-world applications. In this article, we will compare four fractions: $\frac{19}{6}$, $\frac{13}{3}$, $\frac{26}{9}$, and $\frac{47}{12}$, to determine which one is greater than $\frac{33}{8}$. We will use various methods to compare these fractions, including converting them to equivalent decimals and using a number line.

Understanding the Problem

To compare fractions, we need to understand the concept of equivalent fractions. Equivalent fractions are fractions that have the same value, but with different numerators and denominators. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions because they have the same value, but with different numerators and denominators.

Converting Fractions to Equivalent Decimals

One way to compare fractions is to convert them to equivalent decimals. To convert a fraction to a decimal, we divide the numerator by the denominator. For example, to convert $\frac{19}{6}$ to a decimal, we divide 19 by 6, which gives us 3.1667.

Using a Number Line

Another way to compare fractions is to use a number line. A number line is a visual representation of numbers on a line, with each number represented by a point on the line. To compare fractions using a number line, we need to find the equivalent decimal for each fraction and plot the points on the number line.

Comparing Fractions

Now that we have converted the fractions to equivalent decimals and plotted the points on the number line, we can compare them. To compare fractions, we need to determine which point on the number line is greater than the other points.

Conclusion

Based on the equivalent decimals and the number line, we can conclude that $\frac{13}{3}$ is greater than $\frac{33}{8}$. Therefore, the correct answer is B. $\frac{13}{3}$.

Why is $\frac{13}{3}$ Greater than $\frac{33}{8}$?

$\frac{13}{3}$ is greater than $\frac{33}{8}$ because the numerator of $\frac{13}{3}$ is greater than the numerator of $\frac{33}{8}$. To compare fractions, we need to compare the numerators and denominators separately. In this case, the numerator of $\frac{13}{3}$ is 13, which is greater than the numerator of $\frac{33}{8}$, which is 33. However, the denominator of $\frac{13}{3}$ is 3, which is less than the denominator of $\frac{33}{8}$, which is 8. To compare fractions, we need to divide the numerator by the denominator. In this case, $\frac{13}{3}$ is greater than $\frac{33}{8}$ because 13 divided by 3 is greater than 33 divided by 8.

Real-World Applications

Comparing fractions is an essential skill in mathematics, and it's often used in various real-world applications. For example, in cooking, we need to compare fractions to determine the amount of ingredients to use. In finance, we need to compare fractions to determine the interest rate on a loan. In science, we need to compare fractions to determine the concentration of a solution.

Conclusion

In conclusion, comparing fractions is an essential skill in mathematics, and it's often used in various real-world applications. In this article, we compared four fractions: $\frac{19}{6}$, $\frac{13}{3}$, $\frac{26}{9}$, and $\frac{47}{12}$, to determine which one is greater than $\frac{33}{8}$. We used various methods to compare these fractions, including converting them to equivalent decimals and using a number line. Based on the equivalent decimals and the number line, we can conclude that $\frac{13}{3}$ is greater than $\frac{33}{8}$. Therefore, the correct answer is B. $\frac{13}{3}$.

Q: What is the best way to compare fractions?

A: There are several ways to compare fractions, including converting them to equivalent decimals and using a number line. Converting fractions to equivalent decimals is a good way to compare fractions because it allows us to see the fractions in a more familiar format. Using a number line is also a good way to compare fractions because it allows us to visualize the fractions and see which one is greater.

Q: How do I convert a fraction to an equivalent decimal?

A: To convert a fraction to an equivalent decimal, you need to 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 gives you 0.5.

Q: What is a number line?

A: A number line is a visual representation of numbers on a line, with each number represented by a point on the line. Number lines are useful for comparing fractions because they allow us to visualize the fractions and see which one is greater.

Q: How do I use a number line to compare fractions?

A: To use a number line to compare fractions, you need to plot the fractions on the number line and then compare the points. For example, if you have two fractions, $\frac{1}{2}$ and $\frac{1}{3}$, you would plot the points on the number line and then compare the points to see which one is greater.

Q: What is the difference between equivalent fractions and equivalent decimals?

A: Equivalent fractions are fractions that have the same value, but with different numerators and denominators. Equivalent decimals are decimals that have the same value, but with different numbers of decimal places. For example, the fractions $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions because they have the same value, but with different numerators and denominators. The decimals 0.5 and 0.5 are equivalent decimals because they have the same value, but with different numbers of decimal places.

Q: How do I compare fractions with different denominators?

A: To compare fractions with different denominators, you need to find the least common multiple (LCM) of the denominators and then convert the fractions to have the same denominator. For example, if you have two fractions, $\frac{1}{2}$ and $\frac{1}{3}$, you would find the LCM of 2 and 3, which is 6, and then convert the fractions to have the same denominator.

Q: What is the least common multiple (LCM)?

A: The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers. For example, the LCM of 2 and 3 is 6 because 6 is the smallest number that is a multiple of both 2 and 3.

Q: How do I find the LCM of two numbers?

A: To find the LCM of two numbers, you need to list the multiples of each number and then find the smallest number that is a multiple of both numbers. For example, to find the LCM of 2 and 3, you would list the multiples of 2 and 3 and then find the smallest number that is a multiple of both numbers.

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

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers. A decimal is a way of expressing a number as a point followed by one or more digits. For example, the fraction $\frac{1}{2}$ is equal to the decimal 0.5.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, you need to 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 gives you 0.5.

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a way of expressing a number as a combination of a whole number and a fraction. An improper fraction is a way of expressing a number as a fraction with a numerator that is greater than the denominator. For example, the mixed number 2$\frac{1}{2}$ is equal to the improper fraction $\frac{5}{2}$.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and then add the numerator. For example, to convert the mixed number 2$\frac{1}{2}$ to an improper fraction, you would multiply 2 by 2 and then add 1, which gives you $\frac{5}{2}$.

Q: What is the difference between a proper fraction and an improper fraction?

A: A proper fraction is a way of expressing a number as a fraction with a numerator that is less than the denominator. An improper fraction is a way of expressing a number as a fraction with a numerator that is greater than the denominator. For example, the proper fraction $\frac{1}{2}$ is equal to the improper fraction $\frac{5}{2}$.

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

A: To convert an improper fraction to a proper fraction, you need to divide the numerator by the denominator. For example, to convert the improper fraction $\frac{5}{2}$ to a proper fraction, you would divide 5 by 2, which gives you 2$\frac{1}{2}$.