To find the expressions equivalent to \(\frac { - 5} { 19} \), we need to identify expressions that simplify to the same value.

• \(\frac { - 5} { 19} \) is already in its simplest form.
• \(\frac { 6} { 19} \) is not equivalent because both the numerator and denominator are different.
• \(\frac { - 5} { - 19} \) is not equivalent because it simplifies to \(\frac { 5} { 19} \) (positive).
• \(\frac { 6} { - 19} \) is not equivalent because both the numerator and denominator are different.
• \(- \left ( \frac { 5} { 19} \right ) \) is equivalent to \(\frac { - 5} { 19} \).
• \(- \left ( \frac { - 5} { 19} \right ) \) is not equivalent because it simplifies to \(\frac { 5} { 19} \) (positive).

Supplemental Knowledge

• In algebra, equivalent expressions are different expressions that represent the same value. When dealing with fractions and negative signs, it's important to understand how these signs affect the overall value of the expression.
• Negative Signs in Fractions: A negative sign can be placed in front of the entire fraction, in the numerator, or in the denominator. All these placements will yield equivalent values as long as only one negative sign is present.
  • For example, \(- \frac { a} { b} \), \(\frac { - a} { b} \), and \(\frac { a} { - b} \) are all equivalent.
• Simplifying Expressions: Ensure that any simplification or transformation maintains the equality of the expressions.

From Concepts to Reality

Consider a scenario where you owe money to a friend. If you owe $5 to your friend, this can be represented as -5 dollars. Whether you say "I owe 5 dollars" or "I have a debt of 5 dollars," both statements mean the same thing. Similarly, in algebra, different expressions can represent the same value.
Understanding equivalent expressions is fundamental for solving equations and simplifying complex mathematical problems, as it ensures different forms of an expression represent equal quantities.

Mastering algebraic concepts like equivalent expressions is essential for success in mathematics. At UpStudy, we provide interactive tools and resources to help you understand and apply these concepts effectively.For further assistance with understanding algebraic expressions or any other academic challenges, check out UpStudy’s Algebra calculator!
Visit UpStudy today to explore our extensive question bank and personalized learning tools that make mastering algebra both effective and enjoyable!