Add and subtract rational numbers

Learning Objectives Identify rational numbers and express them in various forms (fractions, decimals, mixed numbers). Find the least common denominator (LCD) for two or more rational numbers. Add and subtract fractions with like and unlike denominators. Add and subtract mixed numbers by converting them to improper fractions or using alternative methods. Perform addition and subtraction of rational numbers involving positive and negative values. Solve real-world problems that require adding and subtracting rational numbers. Ever wondered how bakers precisely measure ingredients or how engineers calculate distances with fractions? 🍰📏 Adding and subtracting rational numbers is key! In this lesson, you'll master the essential skills of adding and subtracting rational num...

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, mixed numbers, and terminating or repeating decimals.$5$, $-0.75$, $\frac{2}{3}$, $1\frac{1}{2}$, $0.\overline{3}$ are all rational numbers. NumeratorThe top number in a fraction, which indicates how many parts of the whole are being considered.In the fraction $\frac{3}{4}$, the numerator is $3$. DenominatorThe bottom number in a fraction, which indicates the total number of equal parts the whole is divided into.In the fraction $\frac{3}{4}$, the denominator is $4$. Common DenominatorA shared denominator for two or more fractions, necessary before adding or subtracting them. It is a common multiple of the or...

Adding/Subtracting Rational Numbers with a Common Denominator $\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}$ When rational numbers (fractions) have the same denominator, simply add or subtract their numerators and keep the common denominator. Remember to simplify the result if possible. Adding/Subtracting Rational Numbers with Different Denominators To add or subtract $\frac{a}{b} \pm \frac{c}{d}$: \n 1. Find the Least Common Denominator (LCD) of $b$ and $d$. \n 2. Rewrite each fraction as an equivalent fraction with the LCD as the new denominator. \n 3. Add or subtract the numerators, keeping the LCD. \n 4. Simplify the resulting fraction. This rule ensures that you are adding or subtracting parts of the same size. The LCD is the most efficient common denominator to use....