True Or False?$\[ \frac{21}{25} - \frac{6}{25} = \frac{15}{25} = \frac{3}{5} \\]A. True B. False

Introduction

Mathematics is a subject that deals with numbers, quantities, and shapes. It is a fundamental subject that is used in various fields such as science, engineering, economics, and finance. One of the key concepts in mathematics is fractions, which are used to represent a part of a whole. In this article, we will discuss the concept of simplifying fractions and evaluate the statement: $\frac{21}{25} - \frac{6}{25} = \frac{15}{25} = \frac{3}{5}$.

Understanding Fractions

A fraction is a way of expressing a part of a whole as a ratio of two numbers. It consists of a numerator and a denominator. The numerator represents the number of equal parts, while the denominator represents the total number of parts. For example, the fraction $\frac{1}{2}$ represents one half of a whole.

Simplifying Fractions

Simplifying fractions involves reducing a fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder. For example, the fraction $\frac{6}{8}$ can be simplified by dividing both the numerator and the denominator by their GCD, which is 2. This results in the simplified fraction $\frac{3}{4}$.

Evaluating the Statement

Now, let's evaluate the statement: $\frac{21}{25} - \frac{6}{25} = \frac{15}{25} = \frac{3}{5}$. To do this, we need to simplify the fractions involved.

Step 1: Simplify the first fraction

The first fraction is $\frac{21}{25}$. This fraction cannot be simplified further because 21 and 25 have no common factors other than 1.

Step 2: Simplify the second fraction

The second fraction is $\frac{6}{25}$. This fraction cannot be simplified further because 6 and 25 have no common factors other than 1.

Step 3: Subtract the second fraction from the first fraction

To subtract the second fraction from the first fraction, we need to have the same denominator. In this case, the denominator is 25. So, we can subtract the second fraction from the first fraction as follows:

$\frac{21}{25} - \frac{6}{25} = \frac{21-6}{25} = \frac{15}{25}$

Step 4: Simplify the resulting fraction

The resulting fraction is $\frac{15}{25}$. This fraction can be simplified by dividing both the numerator and the denominator by their GCD, which is 5. This results in the simplified fraction $\frac{3}{5}$.

Conclusion

In conclusion, the statement $\frac{21}{25} - \frac{6}{25} = \frac{15}{25} = \frac{3}{5}$ is TRUE. The first step in evaluating this statement was to simplify the fractions involved. We found that the first fraction $\frac{21}{25}$ cannot be simplified further, while the second fraction $\frac{6}{25}$ also cannot be simplified further. We then subtracted the second fraction from the first fraction to get the resulting fraction $\frac{15}{25}$. Finally, we simplified the resulting fraction by dividing both the numerator and the denominator by their GCD, which is 5. This resulted in the simplified fraction $\frac{3}{5}$, which is equal to the original resulting fraction $\frac{15}{25}$.

Final Answer

The final answer is: A. True

Discussion

This problem is a great example of how to simplify fractions and evaluate mathematical statements. It requires the student to understand the concept of fractions, simplifying fractions, and evaluating mathematical statements. The student must also be able to perform arithmetic operations such as subtraction and division.

Related Problems

• Simplify the fraction $\frac{12}{16}$.
• Evaluate the statement $\frac{7}{9} - \frac{2}{9} = \frac{5}{9} = \frac{1}{3}$.
• Simplify the fraction $\frac{24}{32}$.

References

• [1] "Mathematics for Dummies" by Mark Ryan
• [2] "Algebra and Trigonometry" by James Stewart
• [3] "Mathematics for Elementary Teachers" by Gary L. Musser

Note: The references provided are for educational purposes only and are not intended to be a comprehensive list of resources.

Introduction

In our previous article, we discussed the concept of simplifying fractions and evaluated the statement: $\frac{21}{25} - \frac{6}{25} = \frac{15}{25} = \frac{3}{5}$. We found that the statement is TRUE. In this article, we will provide a Q&A section to help students understand the concept of simplifying fractions and evaluate mathematical statements.

Q&A

Q1: What is a fraction?

A1: A fraction is a way of expressing a part of a whole as a ratio of two numbers. It consists of a numerator and a denominator. The numerator represents the number of equal parts, while the denominator represents the total number of parts.

Q2: How do I simplify a fraction?

A2: To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.

Q3: What is the greatest common divisor (GCD)?

A3: The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder. For example, the GCD of 12 and 16 is 4.

Q4: How do I subtract fractions with different denominators?

A4: To subtract fractions with different denominators, you need to have the same denominator. You can do this by finding the least common multiple (LCM) of the two denominators and then converting both fractions to have the LCM as the denominator.

Q5: What is the least common multiple (LCM)?

A5: The LCM is the smallest number that is a multiple of both numbers. For example, the LCM of 2 and 3 is 6.

Q6: How do I evaluate a mathematical statement?

A6: To evaluate a mathematical statement, you need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q7: What is the final answer to the statement $\frac{21}{25} - \frac{6}{25} = \frac{15}{25} = \frac{3}{5}$?

A7: The final answer is TRUE.

Conclusion

In conclusion, simplifying fractions and evaluating mathematical statements are essential skills in mathematics. By understanding the concept of fractions, simplifying fractions, and evaluating mathematical statements, students can solve problems and answer questions with confidence.

Final Answer

The final answer is: A. True

Discussion

This Q&A section is designed to help students understand the concept of simplifying fractions and evaluate mathematical statements. It requires the student to understand the concept of fractions, simplifying fractions, and evaluating mathematical statements. The student must also be able to perform arithmetic operations such as subtraction and division.

Related Problems

• Simplify the fraction $\frac{12}{16}$.
• Evaluate the statement $\frac{7}{9} - \frac{2}{9} = \frac{5}{9} = \frac{1}{3}$.
• Simplify the fraction $\frac{24}{32}$.

References

• [1] "Mathematics for Dummies" by Mark Ryan
• [2] "Algebra and Trigonometry" by James Stewart
• [3] "Mathematics for Elementary Teachers" by Gary L. Musser

Note: The references provided are for educational purposes only and are not intended to be a comprehensive list of resources.