Perform multiple operations with fractions

Learning Objectives Apply the order of operations (PEMDAS/BODMAS) to expressions involving fractions. Accurately add, subtract, multiply, and divide fractions within a single multi-step expression. Convert between mixed numbers and improper fractions as needed to simplify calculations. Simplify fractional answers to their lowest terms. Solve multi-step problems involving fractions, demonstrating a clear understanding of each operation. Identify and correct common errors when performing multiple operations with fractions. Ever tried following a recipe that asks you to add ingredients like '1/2 cup flour, then 1/4 of the remaining sugar, then divide by 2 for smaller portions'? 🍰 It can get tricky fast! In this lesson, you'll learn how to tackle math problems t...

TermDefinitionExample FractionA number that represents a part of a whole, written as a numerator over a denominator.In the fraction $\frac{3}{4}$, 3 is the numerator and 4 is the denominator, meaning 3 out of 4 equal parts. Improper FractionA fraction where the numerator is greater than or equal to the denominator, representing a value of one or more whole units.$\frac{7}{3}$ is an improper fraction because 7 is greater than 3. It is equivalent to $2\frac{1}{3}$. Mixed NumberA number consisting of a whole number and a proper fraction.$2\frac{1}{3}$ is a mixed number, combining the whole number 2 and the fraction $\frac{1}{3}$. ReciprocalThe reciprocal of a fraction is obtained by flipping the numerator and the denominator. It's used in division of fractions.The reciprocal of $\frac{2...

Order of Operations (PEMDAS/BODMAS) 1. Parentheses/Brackets 2. Exponents/Orders 3. Multiplication and Division (from left to right) 4. Addition and Subtraction (from left to right) This rule applies to all mathematical expressions, including those with fractions, ensuring a consistent approach to solving multi-operation problems. Adding/Subtracting Fractions To add or subtract fractions, they must have a common denominator. If $\frac{a}{b}$ and $\frac{c}{d}$ are fractions, then $\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}$ (after finding a common denominator). Find the Least Common Multiple (LCM) of the denominators, convert fractions to equivalent fractions with the LCM as the new denominator, then add or subtract the numerators. Multiplying Fractions To multip...