Which Sign Makes The Statement True? 3 4 − 2 4 ? 1 4 \frac{3}{4} - \frac{2}{4} \, ? \, \frac{1}{4} 4 3 − 4 2 ? 4 1 A. >B. <C. =

Mar 8, 2025 by ADMIN 134 views

Which Sign Makes the Statement True?

Introduction

In mathematics, we often come across expressions that involve fractions and operations like addition, subtraction, multiplication, and division. When dealing with fractions, it's essential to understand the rules of operations to determine the correct result. In this article, we will explore the given expression $\frac{3}{4} - \frac{2}{4} \, ? \, \frac{1}{4}$ and determine which sign makes the statement true.

Understanding the Expression

The given expression involves two fractions, $\frac{3}{4}$ and $\frac{2}{4}$ , which are being subtracted. The result of this subtraction is then compared to $\frac{1}{4}$ . To evaluate this expression, we need to follow the order of operations (PEMDAS):

Parentheses: There are no parentheses in the expression.
Exponents: There are no exponents in the expression.
Multiplication and Division: Since there are no multiplication or division operations in the expression, we can skip this step.
Addition and Subtraction: This is the step where we perform the subtraction operation.

Evaluating the Expression

To evaluate the expression, we need to subtract $\frac{2}{4}$ from $\frac{3}{4}$ . To do this, we can find a common denominator, which is 4 in this case. We can then subtract the numerators while keeping the denominator the same:

$\frac{3}{4} - \frac{2}{4} = \frac{3-2}{4} = \frac{1}{4}$

Comparing the Results

Now that we have evaluated the expression, we can compare the result to $\frac{1}{4}$ . Since the result of the subtraction is equal to $\frac{1}{4}$ , we can conclude that the statement is true.

Determining the Correct Sign

The question asks which sign makes the statement true. Based on our evaluation, we can see that the statement is true when the result of the subtraction is equal to $\frac{1}{4}$ . Therefore, the correct sign is C. =.

Conclusion

In conclusion, the correct sign that makes the statement true is C. =. This is because the result of the subtraction is equal to $\frac{1}{4}$ , which is the same as the value being compared. Understanding the rules of operations and following the order of operations is crucial in evaluating expressions like this one.

Frequently Asked Questions

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when there are multiple operations in an expression. The order of operations is PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I evaluate an expression with fractions?

A: To evaluate an expression with fractions, you need to follow the order of operations. First, find a common denominator for the fractions. Then, perform the operations indicated in the expression (e.g., addition, subtraction, multiplication, or division).

Q: What is the difference between a numerator and a denominator?

A: The numerator is the number on top of a fraction, and the denominator is the number on the bottom. For example, in the fraction $\frac{3}{4}$ , 3 is the numerator and 4 is the denominator.

Additional Resources

Final Thoughts

Introduction

Fractions and operations can be a challenging topic for many students. In this article, we will address some of the most frequently asked questions related to fractions and operations, providing clear and concise answers to help you better understand these concepts.

Q&A

Q: What is a fraction?

A: A fraction is a way to represent a part of a whole. It consists of two parts: the numerator (the number on top) and the denominator (the number on the bottom). For example, in the fraction $\frac{3}{4}$ , 3 is the numerator and 4 is the denominator.

Q: What is the difference between a numerator and a denominator?

A: The numerator is the number on top of a fraction, and the denominator is the number on the bottom. For example, in the fraction $\frac{3}{4}$ , 3 is the numerator and 4 is the denominator.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find a common denominator. The common denominator is the smallest number that both denominators can divide into evenly. Once you have found the common denominator, you can rewrite each fraction with the common denominator and then add the numerators.

Q: How do I subtract fractions with different denominators?

A: To subtract fractions with different denominators, you need to find a common denominator. The common denominator is the smallest number that both denominators can divide into evenly. Once you have found the common denominator, you can rewrite each fraction with the common denominator and then subtract the numerators.

Q: What is the order of operations?

Q: How do I evaluate an expression with fractions?

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

A: A mixed number is a combination of a whole number and a fraction. For example, 2 $\frac{1}{4}$ is a mixed number. An improper fraction is a fraction where the numerator is greater than the denominator. For example, $\frac{5}{4}$ is an improper fraction.

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. The result is the new numerator, and the denominator remains the same.

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

A: To convert an improper fraction to a mixed number, you need to divide the numerator by the denominator. The result is the whole number, and the remainder is the new numerator.

Additional Resources

Final Thoughts

In conclusion, understanding fractions and operations is crucial for success in mathematics. By following the order of operations and using the correct techniques for adding, subtracting, multiplying, and dividing fractions, you can confidently evaluate expressions and solve problems. Remember to practice regularly and seek help when needed to become proficient in these concepts.

Common Mistakes to Avoid

Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when evaluating expressions with multiple operations.
Not finding a common denominator: When adding or subtracting fractions with different denominators, make sure to find a common denominator before performing the operation.
Not converting mixed numbers to improper fractions: When working with mixed numbers, make sure to convert them to improper fractions before performing operations.
Not converting improper fractions to mixed numbers: When working with improper fractions, make sure to convert them to mixed numbers before performing operations.