Order of operations with rational numbers

Learning Objectives Apply the order of operations (BEDMAS/PEMDAS) to expressions involving fractions, decimals, and integers. Evaluate expressions with nested brackets and multiple operations on rational numbers. Simplify complex fractions by applying the order of operations to the numerator and denominator separately. Solve multi-step problems involving rational numbers by correctly sequencing all operations. Strategically convert between fractions and decimals within a single expression to simplify calculations. Accurately compute expressions involving exponents with rational bases. Ever tried to calculate a 20% tip on a bill that was split three ways after using a $10.50 coupon? 🤔 That's the order of operations in action! This tutorial builds on your knowledge of B...

TermDefinitionExample Rational NumberAny number that can be expressed as a fraction a/b, where 'a' and 'b' are integers and 'b' is not zero. This includes integers, fractions, and decimals that terminate or repeat.-7, 3/5, 0.6, -1.333... Order of OperationsThe universally agreed-upon sequence for performing operations in a mathematical expression to ensure a single, correct result.In 2 + 3 * 4, multiplication is done before addition, resulting in 14, not 20. BEDMAS / PEMDASAn acronym to remember the order of operations: Brackets/Parentheses, Exponents, Division & Multiplication (from left to right), Addition & Subtraction (from left to right).For (5-1)^2 ÷ 2, we do Brackets (4), then Exponents (16), then Division (8). ReciprocalThe multiplicative inve...

The Order of Operations (BEDMAS) 1. (B)rackets 2. (E)xponents 3. (D)ivision & (M)ultiplication [Left to Right] 4. (A)ddition & (S)ubtraction [Left to Right] This is the fundamental hierarchy for simplifying any mathematical expression. Always work through the steps in this order. Remember that Division/Multiplication and Addition/Subtraction are pairs of equal importance; you perform them as they appear from left to right. Exponent Rule for Rational Numbers (a/b)^n = a^n / b^n When a fraction is raised to a power, the exponent applies to both the numerator and the denominator individually. This is a key part of the 'E' step in BEDMAS. Division of Fractions a/b ÷ c/d = a/b * d/c To divide by a fraction, you multiply by its reciprocal. This is how...