What Is The Difference Between The Following Two Numbers?$\frac{3}{4}$ And $\frac{8}{11}$A. $\frac{5}{7}$ B. $\frac{1}{4}$ C. $\frac{1}{44}$ D. $\frac{11}{15}$

Understanding the Difference Between Two Fractions: A Mathematical Analysis

Fractions are a fundamental concept in mathematics, representing a part of a whole. They are used to express ratios, proportions, and relationships between numbers. In this article, we will explore the difference between two fractions, $\frac{3}{4}$ and $\frac{8}{11}$, and compare them with the given options to determine which one is the correct answer.

A fraction is a way of expressing a part of a whole as a ratio of two numbers. It consists of a numerator (the top number) and a denominator (the bottom number). The numerator represents the number of equal parts, while the denominator represents the total number of parts. For example, the fraction $\frac{3}{4}$ represents three equal parts out of a total of four parts.

To compare two fractions, we need to find a common denominator. The common denominator is the smallest number that both denominators can divide into evenly. Once we have a common denominator, we can compare the numerators to determine which fraction is larger.

To find the difference between two fractions, we can subtract the smaller fraction from the larger fraction. However, we need to make sure that the fractions have a common denominator before we can subtract them.

Let's calculate the difference between $\frac{3}{4}$ and $\frac{8}{11}$. To do this, we need to find a common denominator. The least common multiple (LCM) of 4 and 11 is 44. We can rewrite both fractions with a denominator of 44:

$\frac{3}{4} = \frac{3 \times 11}{4 \times 11} = \frac{33}{44}$

$\frac{8}{11} = \frac{8 \times 4}{11 \times 4} = \frac{32}{44}$

Now that we have a common denominator, we can subtract the smaller fraction from the larger fraction:

$\frac{33}{44} - \frac{32}{44} = \frac{1}{44}$

Now that we have calculated the difference between $\frac{3}{4}$ and $\frac{8}{11}$, we can compare it with the given options:

A. $\frac{5}{7}$ B. $\frac{1}{4}$ C. $\frac{1}{44}$ D. $\frac{11}{15}$

The correct answer is C. $\frac{1}{44}$, which is the difference between $\frac{3}{4}$ and $\frac{8}{11}$.

In conclusion, comparing fractions requires finding a common denominator and then comparing the numerators. To find the difference between two fractions, we can subtract the smaller fraction from the larger fraction. In this article, we calculated the difference between $\frac{3}{4}$ and $\frac{8}{11}$ and compared it with the given options to determine which one is the correct answer.

The final answer is C. $\frac{1}{44}$.
Frequently Asked Questions: Understanding Fractions and Their Differences

In our previous article, we explored the difference between two fractions, $\frac{3}{4}$ and $\frac{8}{11}$. We calculated the difference and compared it with the given options to determine which one is the correct answer. In this article, we will answer some frequently asked questions related to fractions and their differences.

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers, while a decimal is a way of expressing a number as a sum of powers of 10. For example, the fraction $\frac{3}{4}$ is equal to the decimal 0.75.

A: To compare two fractions, you need to find a common denominator. The common denominator is the smallest number that both denominators can divide into evenly. Once you have a common denominator, you can compare the numerators to determine which fraction is larger.

A: The least common multiple (LCM) is the smallest number that two or more numbers can divide into evenly. For example, the LCM of 4 and 11 is 44.

A: To find the difference between two fractions, you need to subtract the smaller fraction from the larger fraction. However, you need to make sure that the fractions have a common denominator before you can subtract them.

A: To find the difference between $\frac{1}{2}$ and $\frac{1}{3}$, we need to find a common denominator. The LCM of 2 and 3 is 6. We can rewrite both fractions with a denominator of 6:

$\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$

$\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}$

Now that we have a common denominator, we can subtract the smaller fraction from the larger fraction:

$\frac{3}{6} - \frac{2}{6} = \frac{1}{6}$

A: To find the difference between $\frac{2}{3}$ and $\frac{3}{4}$, we need to find a common denominator. The LCM of 3 and 4 is 12. We can rewrite both fractions with a denominator of 12:

$\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$

$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$

Now that we have a common denominator, we can subtract the smaller fraction from the larger fraction:

$\frac{9}{12} - \frac{8}{12} = \frac{1}{12}$

In conclusion, understanding fractions and their differences requires finding a common denominator and then comparing the numerators. We have answered some frequently asked questions related to fractions and their differences, and provided examples to illustrate the concepts.

The final answer is that the difference between two fractions can be found by subtracting the smaller fraction from the larger fraction, as long as the fractions have a common denominator.