Multiply and divide rational numbers

Learning Objectives Define rational numbers and identify their components. Multiply two or more rational numbers, including fractions, decimals, and mixed numbers. Divide two rational numbers, including fractions, decimals, and mixed numbers. Correctly apply the rules of signs for multiplication and division of rational numbers. Simplify rational expressions involving multiplication and division to their lowest terms. Solve real-world problems that require multiplying and dividing rational numbers. Ever wonder how chefs adjust recipes for different serving sizes, or how engineers calculate material needs for a fraction of a project? 🧑‍🍳📐 It all involves multiplying and dividing parts of numbers! In this lesson, you'll learn the essential rules and techniques for mul...

TermDefinitionExample Rational NumberA number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q$ is not zero. This includes integers, fractions, and terminating or repeating decimals.$\frac{3}{4}$, $-5$, $0.25$ (which is $\frac{1}{4}$), $1.\overline{3}$ (which is $\frac{4}{3}$) NumeratorThe top number in a fraction, representing the number of parts being considered.In the fraction $\frac{5}{8}$, the numerator is $5$. DenominatorThe bottom number in a fraction, representing the total number of equal parts into which the whole is divided.In the fraction $\frac{5}{8}$, the denominator is $8$. ReciprocalThe number by which another number must be multiplied to produce $1$. For a fraction $\frac{a}{b}$, its reciprocal is $\frac{b}{a}$.The reciprocal of $\fr...

Multiplication of Rational Numbers (Fractions) $\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$ To multiply two fractions, multiply their numerators to get the new numerator, and multiply their denominators to get the new denominator. Always simplify the resulting fraction if possible. Division of Rational Numbers (Fractions) $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c}$ To divide by a fraction, multiply the first fraction by the reciprocal of the second fraction (the divisor). Then follow the rules for multiplication. Rules of Signs for Multiplication and Division $\text{Positive} \times \text{Positive} = \text{Positive}$ \newline $\text{Negative} \times \text{Negative} = \text{Positive}$ \newline $\text{Positive} \times \text{Negative} =...