SANKALP CLASS Fractions And Decimals Worksheet 1 Solutions

When dealing with fractions, a strong foundational understanding is crucial. In this worksheet, we will delve into the comparison of fractions, specifically focusing on the question: $\frac{3}{4} \ldots \frac{2}{4}$. The goal is to accurately fill in the box with the correct symbol, choosing from >, <, or =. This exercise not only tests your knowledge of basic fraction comparison but also reinforces the core principles that govern how fractions relate to each other. To approach this problem effectively, we need to understand what fractions represent and how their values change based on their numerators and denominators. The denominator indicates the total number of equal parts into which a whole is divided, while the numerator represents the number of these parts we are considering. In our specific case, both fractions have the same denominator, which simplifies the comparison process significantly. When fractions share a common denominator, comparing them becomes as straightforward as comparing their numerators. The fraction with the larger numerator will have a greater value. This concept is fundamental and serves as the basis for more complex fraction operations and comparisons. For instance, if we were to visualize these fractions, we could imagine a pie divided into four equal slices. The fraction $rac{3}{4}$ represents three of these slices, while $\frac{2}{4}$ represents two slices. It becomes immediately clear that having three slices is more than having two slices. This visual analogy helps solidify the understanding of why $\frac{3}{4}$ is greater than $rac{2}{4}$. Moreover, this foundational knowledge extends beyond simple comparisons. It is essential for performing arithmetic operations with fractions, such as addition, subtraction, multiplication, and division. A solid grasp of fraction values and their relative sizes is also critical when simplifying fractions, finding equivalent fractions, and solving equations involving fractions. In more advanced mathematics, understanding fractions is indispensable for working with rational numbers, algebraic expressions, and calculus. The principles learned here lay the groundwork for tackling complex mathematical concepts and problems. Therefore, mastering the basic comparison of fractions, as demonstrated in this worksheet question, is a stepping stone to achieving proficiency in mathematics as a whole. By understanding the relationship between numerators and denominators, students can confidently navigate more challenging problems and build a strong foundation for future learning.

Detailed Solution for Comparing Fractions

To accurately compare the fractions $rac3}{4}$ and $rac{2}{4}$, we must first recognize that both fractions share the same denominator, which is 4. This common denominator simplifies the comparison process because it means that both fractions are dividing a whole into the same number of equal parts. When fractions have the same denominator, comparing their values becomes as simple as comparing their numerators. The numerator represents the number of parts we are considering out of the total number of parts the whole has been divided into. In the case of $rac{3}{4}$, the numerator is 3, which means we are considering 3 parts out of 4. For $rac{2}{4}$, the numerator is 2, indicating we are considering 2 parts out of 4. Since 3 is greater than 2, it follows that $rac{3}{4}$ is greater than $rac{2}{4}$. To further illustrate this, imagine a pizza cut into four equal slices. If you have 3 slices, you have more pizza than if you only have 2 slices. This visual analogy helps to reinforce the concept that a larger numerator (when the denominators are the same) corresponds to a larger fraction. Therefore, the correct symbol to fill in the box between $rac{3}{4}$ and $rac{2}{4}$ is the “greater than” symbol, which is >. So, the correct expression is $rac{3}{4} > rac{2}{4}$. This simple comparison highlights a fundamental rule in fraction arithmetic when comparing fractions with the same denominator, the fraction with the larger numerator is the larger fraction. This principle is crucial for understanding more complex operations involving fractions, such as addition, subtraction, and ordering a set of fractions. Furthermore, this understanding extends to real-world applications where fractions are used to represent proportions and ratios. For example, in cooking, recipes often use fractions to indicate the amount of ingredients needed. Comparing these fractional amounts accurately ensures the recipe turns out correctly. In summary, by focusing on the numerators when the denominators are the same, we can quickly and accurately compare fractions. This basic skill is essential for building a solid foundation in mathematics and for applying mathematical concepts in everyday life. The comparison $rac{3{4} > rac{2}{4}$ serves as a clear example of this principle.

Choosing the Correct Symbol: >

After a thorough comparison of the fractions $rac3}{4}$ and $rac{2}{4}$, it is evident that the correct symbol to use in the box is the “greater than” symbol, denoted as >. This conclusion is derived from the fundamental principle of fraction comparison when fractions share a common denominator, the fraction with the larger numerator is the greater fraction. In this specific case, both fractions have the same denominator, which is 4. This means that both fractions represent parts of a whole that has been divided into four equal portions. The fraction $rac{3{4}$ has a numerator of 3, indicating that we are considering three of these four equal parts. On the other hand, the fraction $rac{2}{4}$ has a numerator of 2, meaning we are considering only two of the four equal parts. Since 3 is greater than 2, it logically follows that having three parts out of four is more than having two parts out of four. Therefore, $rac{3}{4}$ is greater than $rac{2}{4}$. To further solidify this understanding, consider a practical example. Imagine you have a pie that is divided into four equal slices. If you take three slices, you have a larger portion of the pie than someone who takes only two slices. This real-world analogy helps to make the abstract concept of fraction comparison more concrete and relatable. The choice of the > symbol accurately reflects this relationship, indicating that the value of $rac{3}{4}$ is larger than the value of $rac{2}{4}$. This type of comparison is a foundational skill in mathematics, particularly when dealing with rational numbers and proportions. Understanding how to compare fractions is essential for a variety of mathematical operations, including addition, subtraction, multiplication, and division of fractions. It also plays a crucial role in problem-solving scenarios where quantities are expressed as fractions. Moreover, the ability to compare fractions extends beyond the classroom and into everyday life. For instance, when following a recipe, comparing fractional amounts of ingredients is necessary to ensure the correct proportions. In summary, selecting the > symbol to represent the relationship between $rac{3}{4}$ and $rac{2}{4}$ is not only mathematically accurate but also reinforces the basic principles of fraction comparison. This understanding is crucial for building a solid foundation in mathematics and for applying these concepts in practical situations. Thus, the answer is A. >.

Therefore, the final answer is:

A. >