Unit 2: Rational Numbers and Square Roots

Vocabulary practice flashcards covering rational and irrational numbers, fraction and decimal arithmetic, order of operations, and square roots from Sections 2.1 through 2.4.

Irrational Number

A decimal number that goes on forever without a pattern, such as $7.4536118...$, $\text{π}$, or $√{2}$.

Rational Number

Any number that has an ending, can be expressed as a fraction, or is a decimal number that goes on forever with a repeating pattern (e.g., $3$, $6.25$, $8.999...$, $\frac{12}{78}$, $7.\overline{145}$).

Numerator

The top number in a fraction (e.g., $7$ in $\frac{7}{12}$).

Denominator

The bottom number in a fraction (e.g., $12$ in $\frac{7}{12}$).

Converting a Negative Mixed Fraction to an Improper Fraction

A multi-step process where you ignore the negative sign, multiply the whole number by the denominator, add the numerator, place the total over the original denominator, and put the negative sign back on (e.g., $-4\frac{5}{8} = -\frac{37}{8}$).

Equivalent Fractions

Fractions that represent the same value, created by multiplying or dividing both the numerator and the denominator by the same non-zero number (e.g., $\frac{-3}{-4} = \frac{6}{8}$ or $\frac{10}{7} = \frac{100}{70}$).

Brackets with Negative Numbers

Parentheses used in expressions to clearly indicate that a negative sign belongs to a specific number (e.g., $4.2 + (-5.7)$).

Even Number of Negatives Rule (Multiplication and Division)

A rule stating that an even count of negative numbers in multiplication or division will cancel out to give a positive answer (e.g., $(-3) \times (-4) = 12$ or $\frac{-5}{-4} = \frac{5}{4}$).

Odd Number of Negatives Rule (Multiplication and Division)

A rule stating that an odd count of negative numbers in multiplication or division will result in a negative answer (e.g., $(-1)(-2)(-6) = -12$ or $-10(2) = -20$).

Adding the Opposite

A method for solving subtraction problems with negative numbers by replacing subtraction with addition of the opposite number (e.g., $(-5) - 4 = (-5) + (-4) = -9$).

BEDMAS

An acronym for the order of operations: Brackets, Exponents, Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).

Converting an Improper Fraction to a Mixed Fraction

A process where the whole number is determined by how many times the denominator goes into the numerator, the remainder becomes the new numerator, and the denominator stays the same (e.g., $\frac{17}{5} = 3\frac{2}{5}$).

Common Denominator Requirement

The rule that fractions must have the same denominator before they can be added or subtracted, while ensuring the common denominator itself is not added or subtracted.

Reciprocal ("Kiss + Flip")

The inverted form of a fraction used when dividing fractions by turning division into multiplication by the flipped fraction (e.g., $-1\frac{1}{2} \div \left(-2\frac{3}{4}\right) = -\frac{3}{2} \times \left(-\frac{4}{11}\right) = \frac{12}{22}$).

Square Root

The side length of a square given its area, where $\text{Area} = l \times w$ and side length equals $\sqrt{\text{Area}}$.

Perfect Square

A number whose square root results in a whole number or a clean simplified fraction (e.g., $25$, $225$, $\frac{36}{81}$, and $0.36$).

Lowest Terms Requirement for Fraction Square Roots

The rule that fractions must be reduced to lowest terms before determining whether they are perfect squares (e.g., $\frac{4}{10} = \frac{2}{5}$, which is not a perfect square).