Add and subtract rational numbers

Learning Objectives Identify rational numbers in various forms (fractions, decimals, integers). Add and subtract rational numbers with common denominators. Find a common denominator for fractions and use it to add or subtract them. Convert between mixed numbers and improper fractions to facilitate addition and subtraction. Add and subtract rational numbers expressed as decimals, including negative values. Apply rules for adding and subtracting integers to rational numbers. Solve real-world problems involving the addition and subtraction of rational numbers. Ever wonder how chefs adjust recipes or how engineers calculate precise measurements? 🧑‍🍳📐 It all involves adding and subtracting parts of numbers! In this lesson, you'll learn how to confidently add and subtra...

TermDefinitionExample Rational NumberAny number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$.$0.5 = \frac{1}{2}$, $-3 = \frac{-3}{1}$, $2\frac{1}{3} = \frac{7}{3}$ NumeratorThe top number in a fraction, representing the number of parts being considered.In $\frac{3}{4}$, 3 is the numerator. DenominatorThe bottom number in a fraction, representing the total number of equal parts in the whole.In $\frac{3}{4}$, 4 is the denominator. Common DenominatorA shared denominator for two or more fractions, necessary for adding or subtracting them.For $\frac{1}{2}$ and $\frac{1}{3}$, a common denominator is 6. Least Common Multiple (LCM)The smallest positive integer that is a multiple of two or more given integers. Used to find the least common denomin...

Adding/Subtracting Fractions with Common Denominators $\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$ and $\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$ If fractions already have the same denominator, simply add or subtract their numerators and keep the denominator the same. Adding/Subtracting Fractions with Different Denominators Find the Least Common Denominator (LCD), convert fractions to equivalent fractions with the LCD, then add/subtract numerators. Before adding or subtracting fractions with different denominators, you must find a common denominator (preferably the LCD) and rewrite each fraction as an equivalent fraction with that common denominator. Adding/Subtracting Decimals Align the decimal points, then add or subtract as with whole numbers. Apply integer rules fo...