Apply multiplication and division rules

Learning Objectives Identify rational numbers in various forms (fractions, decimals, integers). Apply the rules for multiplying two rational numbers, including those with different signs. Apply the rules for dividing two rational numbers, including those with different signs. Simplify products and quotients of rational numbers to their simplest form. Understand the concept of a reciprocal and its role in division. Solve real-world problems involving multiplication and division of rational numbers. Ever wonder how chefs adjust recipes for more or fewer servings, or how engineers calculate parts of a whole? 🧑‍🍳⚙️ It all involves multiplying and dividing parts of numbers! In this lesson, you'll learn the essential rules for multiplying and dividing rational numbers, whi...

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 fractions, integers, and terminating or repeating decimals.$\frac{3}{4}$, $-0.5$, $7$ (which is $\frac{7}{1}$), $2\frac{1}{3}$ (which is $\frac{7}{3}$) 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 $2$ is $5$. Reciprocal (Multiplicative Inverse)For any non-zero rational number $\frac{a}{b}$, its reciprocal is $\frac{b}{a}$. When a number is multiplied by its reciprocal, the product is always 1.The reciprocal of $\frac{2}{3}$ is $\frac{3}{...

Multiplication of Rational Numbers To multiply two rational numbers $\frac{a}{b}$ and $\frac{c}{d}$, multiply the numerators and multiply the denominators: $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$. Multiply the top numbers together and the bottom numbers together. Remember to apply sign rules: (positive) x (positive) = positive; (negative) x (negative) = positive; (positive) x (negative) = negative. Division of Rational Numbers To divide one rational number $\frac{a}{b}$ by another $\frac{c}{d}$ (where $\frac{c}{d} \neq 0$), multiply the first rational number by the reciprocal of the second: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$. This rule is often remembered as 'Keep, Change, Flip!' Keep the first fraction as it is...