Rational numbers: find the sign

Learning Objectives Identify whether a given rational number is positive, negative, or zero. Apply the rules for multiplying and dividing signed numbers to determine the sign of a product or quotient of rational numbers. Determine the sign of a rational number raised to an integer power. Analyze expressions involving multiple operations with rational numbers to predict the final sign. Explain the sign of a rational number in various forms (fractions, decimals, mixed numbers). Solve problems involving the sign of rational numbers in real-world contexts. Ever wonder how meteorologists predict if the temperature will be above or below freezing? 🌡️ It often comes down to understanding positive and negative numbers! In this lesson, you'll learn how to quickly determine if a...

TermDefinitionExample Rational NumberAny number that can be expressed as a fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.$\frac{3}{4}$, $-0.5$, $7$ (which is $\frac{7}{1}$), $0$ (which is $\frac{0}{1}$). Positive NumberA number greater than zero, located to the right of zero on a number line.$5$, $\frac{1}{2}$, $0.75$, $100$. Negative NumberA number less than zero, located to the left of zero on a number line.$-3$, $-\frac{2}{3}$, $-1.2$, $-25$. ZeroThe number that is neither positive nor negative. It is the origin on the number line.$0$, $\frac{0}{5}$. NumeratorThe top number in a fraction, representing the number of parts being considered.In $\frac{-3}{4}$, the numerator is $-3$. DenominatorThe bottom number in a fraction, representing the total number of equal p...

Sign of a Fraction A fraction $\frac{p}{q}$ is positive if $p$ and $q$ have the same sign. It is negative if $p$ and $q$ have different signs. This rule applies to fractions where the negative sign can be in the numerator, denominator, or in front of the fraction. For example, $\frac{-a}{b} = \frac{a}{-b} = -\frac{a}{b}$. Multiplication and Division of Signed Rational Numbers $(+\text{number}) \times (+\text{number}) = +\text{result}$ $(-\text{number}) \times (-\text{number}) = +\text{result}$ $(+\text{number}) \times (-\text{number}) = -\text{result}$ $(-\text{number}) \times (+\text{number}) = -\text{result}$ The same rules apply for division. When multiplying or dividing two rational numbers, if their signs are the same, the result is positive. If their signs are...