Algebra I - Chapter 7 Vocab

Adding and Subtracting Rational Expressions with Unlike Denominators

1. Find the LCD of the rational expressions. 2. Rewrite each rational expression as an equivalent expression whose denominator is the LCD found in step 1. 3. Add or subtract numerators and write sum or difference over the common denominator. 4. Simplify or write the rational expressions in simplest form.

Direct Variation

'y' varies directly as 'x', or 'y' is directly proportional to 'x', if there is a nonzero constant 'k' such that y = kx

Inverse Variation

'y' varies inversely as 'x', or 'y' is inversely proportional to 'x', if there is a nonzero constant 'k' such that y = k/x

Solving Equations with Rational Expressions

1. Multiply both sides of the equation by the LCD of all rational expressions. 2. Remove any grouping symbols and solve the resulting equation. 3. Check the solution in the original equation.

Proportion

A mathematical statement that two ratios are equal.

Least Common Denominator (LCD)

A polynomial of least degree whose factors include all the factors of the denominators in the list.

Ratio

A quotient of two numbers or two quantities.

Complex Rational Expression or Complex Fraction

A rational expression whose numerator or denominator or both contain fractions.

Rational Expression

An expression that can be written in the form P/Q, where 'P' and 'Q' are polynomials are 'Q' does not equal zero.

Divide Rational Expressions

If P/Q and R/S are rational expressions, then P/Q divided by R/S equals P/Q times S/R which equals PS/QR. Simply multiply the first by the reciprocal of the second.

Multiply Rational Expressions

If P/Q and R/S are rational expressions, then P/Q times R/S equals PR/QS Simply multiply numerators and multiply denominators.

Add and Subtract Rational Expressions with Common Denominators

If P/Q and R/S are rational expressions, then P/R + Q/R = (P+Q)/R and P/R - Q/R = (P-Q)/R Simply add and subtract the numerators and put over the common denominator.

Cross Products

If a/b = c/d, then ad = bc.

Simplify a Complex Fraction

Method 1: Add/subtract fractions in the numerator and in the denominator of the complex fraction, then divide. Method 2: Find the LCD of all fractions, then multiply the numerator and the denominator of the complex fraction by the LCD, finish by performing the indicated operations.

Constant of Variation or Constant of Proportionality

The number 'k' in y = kx and y = k/x

Simplify Rational Expressions

The process of writing rational expressions in lowest terms or simplest form: 1. Completely factor the numerator and denominator 2. Divide out factors common to the numerator and denominator.

Similar Triangles

Triangles that have the same shape but not necessarily the same size. The measures of corresponding angles are equal, and corresponding sides are in proportion.

Undefined Rational Expression

Values that make the deminator zero.