Simplest Form

Definition

The simplest form of a mathematical expression, such as a fraction or an algebraic expression, is the form that uses the fewest possible terms, factors, or digits without changing the value or meaning of the expression. It is the most concise and compact way to represent the expression.

5 Must Know Facts For Your Next Test

1. Simplifying an expression to its simplest form often involves reducing fractions, factoring, and finding the least common denominator.
2. When simplifying a fraction, the goal is to find the equivalent fraction with the smallest possible numerator and denominator.
3. Factoring an algebraic expression can reveal its simplest form by breaking it down into a product of its prime factors.
4. Finding the least common denominator of a set of fractions is a crucial step in simplifying the fractions to a common form.
5. Simplifying expressions to their simplest form makes them easier to understand, manipulate, and work with in further calculations.

Review Questions

• Explain the process of reducing a fraction to its simplest form.
  • To reduce a fraction to its simplest form, you need to find the greatest common factor (GCF) of the numerator and denominator, and then divide both the numerator and denominator by the GCF. This will result in an equivalent fraction with the smallest possible numerator and denominator. For example, to simplify the fraction $\frac{12}{18}$, you would first find the GCF of 12 and 18, which is 6. Then, you would divide both the numerator and denominator by 6 to get the simplified fraction $\frac{2}{3}$.
• Describe how factoring can be used to simplify an algebraic expression.
  • Factoring an algebraic expression can reveal its simplest form by breaking it down into a product of its prime factors. For example, consider the expression $4x^2 - 9$. By factoring, we can rewrite this as $(2x + 3)(2x - 3)$, which is the simplest form of the expression. Factoring allows us to identify the common factors and reduce the expression to the fewest possible terms or factors, making it easier to work with and understand.
• Explain the importance of finding the least common denominator when simplifying a set of fractions.
  • Finding the least common denominator (LCD) of a set of fractions is crucial for simplifying the fractions to a common form. The LCD is the smallest positive integer that is a multiple of all the denominators in the set of fractions. Once the LCD is found, you can rewrite each fraction with the LCD as the denominator, which allows you to perform operations such as addition, subtraction, and comparison on the fractions. Simplifying fractions to a common denominator is an essential step in many algebraic problems, as it ensures that the fractions can be easily manipulated and combined.

Related terms

Equivalent Fractions:

Fractions that have the same value, even though they may have different numerators and denominators.

Factoring:

The process of breaking down an algebraic expression into a product of simpler expressions.

Least Common Denominator (LCD):

The smallest positive integer that is a multiple of all the denominators of a set of fractions.