Apply addition, subtraction, multiplication and division rules

Learning Objectives Identify rational numbers and their different forms (fractions, decimals, mixed numbers). Add and subtract rational numbers, including those with different denominators. Multiply rational numbers, including fractions, decimals, and mixed numbers. Divide rational numbers, understanding the concept of reciprocals. Perform operations with negative rational numbers accurately. Solve multi-step problems involving all four basic operations with rational numbers. Ever wonder how chefs adjust recipes, or how engineers calculate precise measurements for bridges? 🌉 It all comes down to mastering operations with rational numbers! In this lesson, you'll learn and practice the essential rules for adding, subtracting, multiplying, and dividing rational numbers,...

TermDefinitionExample Rational NumberAny number that can be expressed as a fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.$0.5 = \frac{1}{2}$, $-3 = \frac{-3}{1}$, $2\frac{1}{4} = \frac{9}{4}$ NumeratorThe top number in a fraction, representing the number of parts being considered.In $\frac{3}{4}$, the numerator is 3. DenominatorThe bottom number in a fraction, representing the total number of equal parts in the whole.In $\frac{3}{4}$, the denominator is 4. ReciprocalThe multiplicative inverse of a number; when a number is multiplied by its reciprocal, the product is 1.The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$. The reciprocal of 5 is $\frac{1}{5}$. Common DenominatorA shared denominator for two or more fractions, necessary for addition and subtraction.For $\f...

Adding and Subtracting Rational Numbers (Fractions) $\frac{a}{b} \pm \frac{c}{d} = \frac{ad}{bd} \pm \frac{bc}{bd} = \frac{ad \pm bc}{bd}$ To add or subtract fractions, they must have a common denominator. Find the least common multiple (LCM) of the denominators to create equivalent fractions. Then, add or subtract the numerators and keep the common denominator. Always simplify the result. Multiplying 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. Dividing 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...