Rational numbers: find the sign

Learning Objectives Identify positive and negative rational numbers. Determine the sign of a product involving two rational numbers. Determine the sign of a quotient involving two rational numbers. Apply rules for finding the sign of products with multiple rational numbers. Apply rules for finding the sign of quotients with multiple rational numbers. Predict the sign of an expression involving multiplication and division of decimals. Ever wonder how meteorologists predict temperature changes 🌡️ or how accountants track profits and losses 💰? Understanding positive and negative numbers is key! In this lesson, you'll learn how to quickly determine if the result of multiplying or dividing rational numbers (including decimals) will be positive or negative, even before you...

TermDefinitionExample Rational NumberAny number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. Decimals that terminate or repeat are rational numbers.$0.5 = \frac{1}{2}$, $-3 = \frac{-3}{1}$, $0.333... = \frac{1}{3}$ Positive NumberA number greater than zero, typically written without a sign or with a '+' sign.$7$, $0.25$, $\frac{3}{4}$ Negative NumberA number less than zero, always written with a '-' sign.$-5$, $-0.75$, $-\frac{1}{2}$ ProductThe result obtained when two or more numbers are multiplied together.The product of $2$ and $3$ is $6$ ($2 \times 3 = 6$). QuotientThe result obtained when one number is divided by another number.The quotient of $10$ and $2$ is $5$ ($10 \div 2 = 5$). Even NumberAn integer that is d...

Sign Rule for Multiplication/Division of Two Numbers with the Same Sign $(+) \times (+) = (+)$ ; $(-) \times (-) = (+)$ $(+) \div (+) = (+)$ ; $(-) \div (-) = (+)$ If two rational numbers have the same sign (both positive or both negative), their product or quotient will always be positive. Sign Rule for Multiplication/Division of Two Numbers with Different Signs $(+) \times (-) = (-)$ ; $(-) \times (+) = (-)$ $(+) \div (-) = (-)$ ; $(-) \div (+) = (-)$ If two rational numbers have different signs (one positive and one negative), their product or quotient will always be negative. Sign Rule for Multiplication of Multiple Rational Numbers Count the number of negative factors. If there is an *even* number of negative factors in a product, the overall product will be...