Simplify The Expression: $\frac{1}{6} - \frac{4}{15}$

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Introduction

Mathematics is a vast and fascinating field that deals with numbers, quantities, and shapes. It is a fundamental subject that has numerous applications in various aspects of life, including science, technology, engineering, and mathematics (STEM). In mathematics, expressions are used to represent mathematical relationships between variables and constants. One of the essential skills in mathematics is simplifying expressions, which involves reducing complex expressions to their simplest form. In this article, we will focus on simplifying the expression $\frac{1}{6} - \frac{4}{15}$.

Understanding the Expression

The given expression is a subtraction of two fractions: $\frac{1}{6}$ and $\frac{4}{15}$. To simplify this expression, we need to find a common denominator for both fractions. The common denominator is the least common multiple (LCM) of the denominators of the two fractions. In this case, the LCM of 6 and 15 is 30.

Finding the Common Denominator

To find the common denominator, we need to list the multiples of 6 and 15 and find the smallest number that is common to both lists.

• Multiples of 6: 6, 12, 18, 24, 30, ...
• Multiples of 15: 15, 30, 45, 60, ...

As we can see, the smallest number that is common to both lists is 30. Therefore, the common denominator is 30.

Simplifying the Expression

Now that we have found the common denominator, we can rewrite both fractions with the common denominator.

$\frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30}$

$\frac{4}{15} = \frac{4 \times 2}{15 \times 2} = \frac{8}{30}$

Now that both fractions have the same denominator, we can subtract them.

$\frac{5}{30} - \frac{8}{30} = \frac{5 - 8}{30} = \frac{-3}{30}$

Simplifying the Result

The resulting fraction $\frac{-3}{30}$ can be simplified further by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 3 and 30 is 3.

$\frac{-3}{30} = \frac{-3 \div 3}{30 \div 3} = \frac{-1}{10}$

Therefore, the simplified expression is $\frac{-1}{10}$.

Conclusion

Simplifying expressions is an essential skill in mathematics that involves reducing complex expressions to their simplest form. In this article, we have simplified the expression $\frac{1}{6} - \frac{4}{15}$ by finding the common denominator, rewriting both fractions with the common denominator, subtracting them, and simplifying the resulting fraction. The simplified expression is $\frac{-1}{10}$.

Frequently Asked Questions

• What is the common denominator of 6 and 15? The common denominator of 6 and 15 is 30.
• How do I simplify a fraction? To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.
• What is the simplified expression of $\frac{1}{6} - \frac{4}{15}$? The simplified expression of $\frac{1}{6} - \frac{4}{15}$ is $\frac{-1}{10}$.

Further Reading

• Simplifying Fractions: This article provides a comprehensive guide on simplifying fractions, including finding the greatest common divisor (GCD) and dividing both numbers by the GCD.
• Mathematics: This article provides an overview of mathematics, including its history, branches, and applications.
• Expressions: This article provides an overview of expressions, including their types, properties, and operations.
  

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Introduction

In our previous article, we simplified the expression $\frac{1}{6} - \frac{4}{15}$ by finding the common denominator, rewriting both fractions with the common denominator, subtracting them, and simplifying the resulting fraction. In this article, we will answer some frequently asked questions related to simplifying expressions.

Q&A

Q: What is the common denominator of 6 and 15?

A: The common denominator of 6 and 15 is 30.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.

Q: What is the simplified expression of $\frac{1}{6} - \frac{4}{15}$?

A: The simplified expression of $\frac{1}{6} - \frac{4}{15}$ is $\frac{-1}{10}$.

Q: How do I find the greatest common divisor (GCD) of two numbers?

A: To find the GCD of two numbers, you can use the Euclidean algorithm or list the factors of both numbers and find the largest factor that is common to both.

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, while a decimal is a way of expressing a fraction as a number with a point and digits after the point.

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

A: To convert a fraction to a decimal, you can divide the numerator by the denominator.

Q: What is the simplified expression of $\frac{2}{3} + \frac{1}{6}$?

A: To simplify this expression, you need to find the common denominator, which is 6. Then, you can rewrite both fractions with the common denominator and add them.

$\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$

$\frac{1}{6} = \frac{1}{6}$

$\frac{4}{6} + \frac{1}{6} = \frac{4 + 1}{6} = \frac{5}{6}$

Therefore, the simplified expression is $\frac{5}{6}$.

Q: What is the simplified expression of $\frac{3}{4} - \frac{1}{8}$?

A: To simplify this expression, you need to find the common denominator, which is 8. Then, you can rewrite both fractions with the common denominator and subtract them.

$\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$

$\frac{1}{8} = \frac{1}{8}$

$\frac{6}{8} - \frac{1}{8} = \frac{6 - 1}{8} = \frac{5}{8}$

Therefore, the simplified expression is $\frac{5}{8}$.

Conclusion

Simplifying expressions is an essential skill in mathematics that involves reducing complex expressions to their simplest form. In this article, we have answered some frequently asked questions related to simplifying expressions, including finding the common denominator, simplifying fractions, and converting fractions to decimals.

Frequently Asked Questions

• What is the common denominator of 6 and 15? The common denominator of 6 and 15 is 30.
• How do I simplify a fraction? To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.
• What is the simplified expression of $\frac{1}{6} - \frac{4}{15}$? The simplified expression of $\frac{1}{6} - \frac{4}{15}$ is $\frac{-1}{10}$.

Further Reading

• Simplifying Fractions: This article provides a comprehensive guide on simplifying fractions, including finding the greatest common divisor (GCD) and dividing both numbers by the GCD.
• Mathematics: This article provides an overview of mathematics, including its history, branches, and applications.
• Expressions: This article provides an overview of expressions, including their types, properties, and operations.