Multiply and divide rational numbers

Learning Objectives Apply multiplication and division rules for rational numbers to solve real-world problems. Translate word problems involving rational numbers into appropriate mathematical expressions. Determine the correct operation (multiplication or division) based on the context of a problem. Perform multi-step calculations with rational numbers accurately. Interpret and state solutions in the context of the original problem. Simplify rational number expressions before or after performing operations. Ever wonder how stores calculate discounts on fractions of an item, or how chefs adjust recipes for half a batch? 🍕 These everyday tasks rely on multiplying and dividing rational numbers! In this lesson, you'll learn how to tackle word problems that involve multipl...

TermDefinitionExample Rational NumberA number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. This includes integers, fractions, mixed numbers, and terminating or repeating decimals.$0.75 = \frac{3}{4}$, $-5 = \frac{-5}{1}$, $1\frac{2}{3} = \frac{5}{3}$ ProductThe result obtained when two or more numbers are multiplied together.The product of $\frac{1}{2}$ and $\frac{3}{4}$ is $\frac{3}{8}$. QuotientThe result obtained when one number is divided by another number.The quotient of $10$ divided by $2.5$ is $4$. ReciprocalTwo numbers are reciprocals if their product is 1. To find the reciprocal of a fraction, you 'flip' the numerator and denominator.The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$. The reciprocal of $5$ (or $\frac{5}{...

Multiplication of Rational Numbers (Fractions) $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$ To multiply fractions, multiply the numerators together and multiply the denominators together. Simplify the resulting fraction if possible. Division of Rational Numbers (Fractions) $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}$ To divide by a fraction, you multiply the first fraction by the reciprocal of the second fraction (Keep, Change, Flip). Multiplication/Division of Rational Numbers (Signs) $\text{Positive} \times \text{Positive} = \text{Positive}$ \newline $\text{Negative} \times \text{Negative} = \text{Positive}$ \newline $\text{Positive} \times \text{Negative} = \text{Negative}$ \newline $\text{Negati...