Apply addition and subtraction rules

Learning Objectives Identify and classify rational numbers, including fractions, decimals, and integers. Add and subtract rational numbers with like denominators. Find the least common denominator (LCD) to add and subtract rational numbers with unlike denominators. Apply the rules for adding and subtracting positive and negative rational numbers. Convert between mixed numbers, improper fractions, and decimals to facilitate addition and subtraction. Solve multi-step problems involving the addition and subtraction of various forms of rational numbers. Ever wonder how much money you have left after buying snacks and paying your friend back? 💸 Understanding how to add and subtract rational numbers helps you manage real-life finances! In this lesson, you'll learn the essen...

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, and terminating or repeating decimals.$0.5 = \frac{1}{2}$, $-3 = \frac{-3}{1}$, $\frac{2}{3}$, $1.25 = \frac{5}{4}$ NumeratorThe top number in a fraction, indicating how many parts of the whole are being considered.In $\frac{3}{4}$, 3 is the numerator. DenominatorThe bottom number in a fraction, indicating the total number of equal parts the whole is divided into.In $\frac{3}{4}$, 4 is the denominator. Common DenominatorA common multiple of the denominators of two or more fractions. It's necessary to have a common denominator before adding or subtracting fractions.For $\frac{1}{2}$ and $\frac{1}{3}$, a common...

Adding Rational Numbers (Same Denominator) $\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$ To add fractions with the same denominator, add the numerators and keep the denominator the same. Remember to simplify the result if possible. Subtracting Rational Numbers (Same Denominator) $\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$ To subtract fractions with the same denominator, subtract the numerators and keep the denominator the same. Simplify the result if possible. Adding/Subtracting Rational Numbers (Different Denominators) $\frac{a}{b} \pm \frac{c}{d} = \frac{a \cdot d}{b \cdot d} \pm \frac{c \cdot b}{d \cdot b} = \frac{ad \pm bc}{bd}$ (using a common denominator, ideally the LCD) To add or subtract fractions with different denominators, first find a common denominator (p...