Multiply and divide rational numbers

Learning Objectives Identify rational numbers in various forms (fractions, decimals, mixed numbers). Multiply two or more rational numbers, including positive and negative values. Divide two or more rational numbers, including positive and negative values. Convert mixed numbers to improper fractions and vice versa to facilitate operations. Simplify rational number products and quotients to their simplest form. Solve real-world problems involving multiplication and division of rational numbers. Ever wondered how chefs adjust recipes for different numbers of servings, or how engineers calculate material usage for scaled models? 📏 These tasks often involve multiplying and dividing fractions and decimals! In this lesson, you'll learn the essential rules and strategies for...

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, terminating decimals, and repeating decimals.$\frac{3}{4}$, $-5$, $0.75$, $2\frac{1}{2}$, $0.\overline{3}$ NumeratorThe top number in a fraction, which indicates how many parts of the whole are being considered.In the fraction $\frac{2}{3}$, the numerator is $2$. DenominatorThe bottom number in a fraction, which indicates the total number of equal parts the whole is divided into.In the fraction $\frac{2}{3}$, the denominator is $3$. ReciprocalThe reciprocal of a non-zero number is $1$ divided by that number. For a fraction $\frac{a}{b}$, its reciprocal is $\frac{b}{a}$.The reciprocal of $\frac{3}{5}$ is $\fra...

Multiplication of Rational Numbers (Fractions) $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$ To multiply two fractions, multiply the numerators together and multiply the denominators together. Simplify the resulting fraction if possible. Remember to convert mixed numbers to improper fractions first. 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, multiply by its reciprocal. This means 'Keep, Change, Flip': Keep the first fraction, Change the division sign to multiplication, and Flip (find the reciprocal of) the second fraction. Then multiply as usual. Sign Rules for Multiplication and Division $(+) \times (+) = (+)$, $(-) \times...