Apply addition and subtraction rules

Learning Objectives Define and identify rational numbers. Add and subtract rational numbers with common denominators. Find the least common denominator (LCD) for rational numbers with different denominators. Add and subtract rational numbers with different denominators by converting them to equivalent fractions with the LCD. Convert between mixed numbers and improper fractions to facilitate addition and subtraction. Apply rules for adding and subtracting positive and negative rational numbers. Solve real-world problems involving the addition and subtraction of rational numbers. Ever wondered how chefs adjust recipes when they need to make half a batch, or how engineers calculate precise measurements for building bridges? 🧑‍🍳📐 It all involves working with parts of a whol...

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.$\frac{3}{4}$, $-5$, $0.75$, $2\frac{1}{2}$ NumeratorThe top number in a fraction, which indicates how many parts of the whole are being considered.In the fraction $\frac{5}{8}$, the numerator is 5. DenominatorThe bottom number in a fraction, which indicates the total number of equal parts the whole is divided into.In the fraction $\frac{5}{8}$, the denominator is 8. Common DenominatorA shared denominator for two or more fractions, which is necessary before you can add or subtract them.For $\frac{1}{2}$ and $\frac{1}{3}$, a common denominator is 6. Least Common Denominat...

Adding Rational Numbers with Common Denominators $\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$ To add fractions with the same denominator, simply add their numerators and keep the common denominator. Always simplify the result if possible. Subtracting Rational Numbers with Common Denominators $\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$ To subtract fractions with the same denominator, subtract the numerators and keep the common denominator. Always simplify the result if possible. Adding/Subtracting Rational Numbers with Different Denominators $\frac{a}{b} \pm \frac{c}{d} = \frac{a \cdot d}{b \cdot d} \pm \frac{c \cdot b}{d \cdot b} = \frac{ad \pm cb}{bd}$ (using common denominator $bd$ or LCD) First, find the Least Common Denominator (LCD) of the fractions. Then, rewrit...