numerator

Examples of numerator in the following topics:

• Complex Fractions

  • A complex fraction is one in which the numerator, denominator, or both are fractions, which can contain variables, constants, or both.
  • Since there are no terms that can be combined or simplified in either the numerator or denominator, we'll skip to Step 3, dividing the numerator by the denominator:
  • Start with Step 1 of the combine-divide method above: combine the terms in the numerator.
  • You'll find that the common denominator of the two fractions in the numerator is 6, and then you can add those two terms together to get a single fraction term in the larger fraction's numerator:
  • Let's turn to Step 3: divide the numerator by the denominator.

• Solving Problems with Rational Functions

  • The $x$-intercepts of rational functions are found by setting the polynomial in the numerator equal to $0$ and solving for $x$.
  • In the case of rational functions, the $x$-intercepts exist when the numerator is equal to $0$.
  • Set the numerator of this rational function equal to zero and solve for $x$:
  • Here, the numerator is a constant, and therefore, cannot be set equal to $0$.
  • Use the numerator of a rational function to solve for its zeros

• Fractions

  • A fraction represents a part of a whole and consists of an integer numerator and a non-zero integer denominator.
  • Then, subtract the numerators.
  • To multiply fractions, simply multiply the numerators by each other and the denominators by each other.
  • To multiply a fraction by a whole number, simply multiply that number by the numerator of the fraction:
  • The reciprocal is simply the fraction turned upside down such that the numerator and denominator switch places.

• Simplifying, Multiplying, and Dividing Rational Expressions

  • Rational expressions can be simplified by factoring the numerator and denominator where possible, and canceling terms.
  • Recall that when two fractions are multiplied together, their numerators are multiplied to yield the numerator of their product, and their denominators are multiplied to yield the denominator of their product.
  • Following the rule for multiplying fractions, simply multiply their respective numerators and denominators:
  • Notice that we multiplied the numerators together and the denominators together, but we did not multiply the numerator by the denominator or vice-versa.
  • Multiplying out the numerator and denominator, this can be written as:

• Asymptotes

  • However, the linear factor $(x-1)$ cancels with a factor in the numerator.
  • The degree of the numerator and degree of the denominator determine whether or not there are any horizontal or oblique asymptotes.
  • The asymptote is the polynomial term after dividing the numerator and denominator, and is a linear expression.
  • Also notice that one linear factor $(x-1)$ cancels with the numerator.
  • The coefficient of the highest power term is $2$ in the numerator and $1$ in the denominator.

• Rational Inequalities

  • The zeros in the numerator are $x$-values at which the rational inequality crosses from negative to positive or from positive to negative.
  • The numerator has zeros at $x=-3$ and $x=1$.
  • In the case of $x=-3$ and $x=1$, the rational function has a numerator equal to zero, which makes the function overall equal to zero, making it inclusive in the solution.
  • For $x$ values that are zeros for the numerator polynomial, the rational function overall is equal to zero.

• Fractions Involving Radicals

  • In mathematics, we are often given terms in the form of fractions with radicals in the numerator and/or denominator.
  • This same principal can be applied to fractions: whatever we do to the numerator, we must also do to the denominator, and vice versa.

• Solving Equations with Rational Expressions; Problems Involving Proportions

  • This leads us to a very general rule: If you have a rational equation where the denominators are the same, then the numerators must be the same.
  • This in turn suggests a strategy: find a common denominator, and then set the numerators equal.
  • Based on the rule above—since the denominators are equal, we can now assume the numerators are equal, so we know that $3x(x-2)= 4x(x+6)$ or, multiplied out, that $3x^2-6x=4x^2+24x$

• Absolute Value

  • Other names for absolute value include "numerical value," "modulus," and "magnitude."

• Rules for Exponent Arithmetic

  • If you have $n$ factors of $a$ in the denominator, then you can cross out $n$ factors from the numerator.
  • If there were $m$ factors in the numerator, now you have $(m-n)$ factors in the numerator.
  • Here you can see that two 3s will cancel out from the numerator and denominator.