Add, subtract, multiply, and divide fractions and mixed numbers: word problems

Learning Objectives Identify the correct mathematical operation (addition, subtraction, multiplication, or division) required to solve fraction and mixed number word problems. Translate real-world scenarios described in word problems into mathematical expressions involving fractions and mixed numbers. Accurately perform addition and subtraction of fractions and mixed numbers within word problem contexts. Accurately perform multiplication and division of fractions and mixed numbers within word problem contexts. Solve multi-step word problems that require a combination of operations with fractions and mixed numbers. Convert between mixed numbers and improper fractions efficiently to simplify calculations in word problems. Interpret fractional answers in the context of the orig...

TermDefinitionExample FractionA number that represents a part of a whole or a collection. It is written as a ratio of two numbers, the numerator and the denominator.In the fraction $\frac{3}{4}$, 3 is the numerator and 4 is the denominator, meaning 3 out of 4 equal parts. Mixed NumberA number consisting of a whole number and a proper fraction.$2\frac{1}{2}$ is a mixed number, representing two whole units and one-half of another unit. 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, which can also be written as the mixed number $2\frac{1}{3}$. Common DenominatorA common multiple of the denominators of two or more fractions, necessary for adding or subtracting t...

Adding/Subtracting Fractions and Mixed Numbers 1. Find a common denominator. 2. Convert fractions to equivalent fractions with the common denominator. 3. Add or subtract the numerators, keeping the denominator the same. 4. Simplify if possible. For mixed numbers, convert to improper fractions first or handle whole numbers and fractions separately. Use this rule when combining quantities or finding the difference between quantities. Remember to convert mixed numbers to improper fractions before finding a common denominator for easier calculation, or ensure you borrow correctly when subtracting fractions. Multiplying Fractions and Mixed Numbers 1. Convert any mixed numbers to improper fractions. 2. Multiply the numerators together. 3. Multiply the denominators together. 4. Simpl...