simplify

(verb)

To make simpler, either by reducing in complexity, reducing to component parts, or making easier to understand.

Related Terms

Examples of simplify in the following topics:

  • Assumptions

    • Economists use assumptions in order to simplify economics processes so that they are easier to understand.
    • Economists use assumptions in order to simplify economic processes so that it is easier to understand.
    • Critics have stated that assumptions cause economists to rely on unrealistic, unverifiable, and highly simplified information that in some cases simplifies the proofs of desired conclusions.
    • Although simplifying can lead to a better understanding of complex phenomena, critics explain that the simplified, unrealistic assumptions cannot be applied to complex, real world situations.
    • Assess the benefits and drawbacks of using simplifying assumptions in economics

  • Simplifying Radical Expressions

    • Radical expressions containing variables can be simplified to a basic expression in a similar way to those involving only integers.
    • A radical expression is said to be in simplified form if:
    • Radical expressions that contain variables are treated just as though they are integers when simplifying the expression.
    • As with numbers with rational exponents, these rules can be helpful in simplifying radical expressions with variables.
    • Notice that the exponent in the denominator can be simplified, so we have $4 \cdot \frac{x^{\frac{7}{2}}}{x^{\frac{1}{2}}}$.

  • Simplifying Exponential Expressions

    • Recall the rules for operating on numbers with exponents, which are used when simplifying and solving problems in mathematics.
    • To simplify the first part of the expression, apply the rule for multiplying two exponential expressions with the same base:
    • To simplify the second part of the expression, apply the rule for multiplying numbers with exponents:
    • Combining the two terms, our original expression simplifies to $a^5 + 8b^6$.

  • Simplifying Algebraic Expressions

    • Algebraic expressions may be simplified, based on the basic properties of arithmetic operations.
    • Now that we understand each of the components of the expression, let's look at how we simplify them.
    • Added terms are simplified using coefficients.
    • For example, $x+x+x$ can be simplified as $3x$ (where 3 is the coefficient).
    • Multiplied terms are simplified using exponents.

  • Complex Fractions

    • When dealing with equations that involve complex fractions, it is useful to simplify the complex fraction before solving the equation.
    • The process of simplifying complex fractions, known as the "combine-divide method," is as follows:
    • Therefore, we use the cancellation method to simplify the numbers as much as possible, and then we multiply by the simplified reciprocal of the divisor, or denominator, fraction:
    • Therefore, the complex fraction $\frac {\left( \frac {8}{15}\right) }{\left( \frac {2}{3}\right)}$ simplifies to $\frac {4}{5}$.
    • To do so, we multiply the fractions in the denominator together and simplify the result by reducing it to lowest terms:

  • Simplifying, Multiplying, and Dividing Rational Expressions

    • Just like a fraction involving numbers, a rational expression can be simplified, multiplied, and divided.
    • The rules for performing these operations often mirror the rules for simplifying, multiplying, and dividing fractions.
    • The latter form is a simplified version of the former graphically.
    • The operations are slightly more complicated, as there may be a need to simplify the resulting expression.
    • Write rational expressions in lowest terms by simplifying them, using the same rules as for fractions

  • Negative Exponents

    • This rule makes it possible to simplify expressions with negative exponents.
    • Therefore, we can simplify the expression inside the parentheses:

  • Rational Exponents

    • Rational exponents are another method for writing radicals and can be used to simplify expressions involving both exponents and roots.
    • We can use this rule to easily simplify a number that has both an exponent and a root.
    • We can simplify the fraction in the exponent to 2, giving us $5^2=25$.

  • Simplifying Expressions of the Form log_a a^x and a(log_a x)

    • The expressions logaax and alogax can be simplified to x, a shortcut in complex equations.

  • Pythagorean Identities

    • The Pythagorean identities are useful in simplifying expressions with trigonometric functions.
    • Let's try to simplify this.
    • The sine functions cancel and this simplifies to $1$, so we have:
    • Simplify the following expression: $5\sin^2 t + \sec^2 t + 5\cos^2 t - 1 - \tan^2 t$
    • The expression $5\sin^2 t + \sec^2 t + 5\cos^2 t - 1 - \tan^2 t$ simplifies to $5$.