Overview
This lesson explains how to divide simple fractions and mixed fractions, including step-by-step procedures, examples, and practice problems.
Dividing Simple Fractions
- To divide fractions, multiply the first fraction (dividend) by the reciprocal of the second fraction (divisor).
- The reciprocal of a fraction is created by switching its numerator and denominator.
- Always write both numbers as fractions before dividing.
- Simplify answers to their lowest terms using cancellation (dividing common factors).
Example Solutions for Simple Fractions
- Example: ( \frac{8}{9} \div \frac{2}{3} = \frac{8}{9} \times \frac{3}{2} ), then cancel and simplify.
- Convert any improper fractions in the answer into mixed numbers.
Dividing Mixed Fractions
- Change mixed numbers to improper fractions by multiplying the whole number by the denominator and adding the numerator.
- Get the reciprocal of the divisor and replace the division sign with multiplication.
- Multiply numerators and denominators, then simplify or convert to a mixed number.
Example Solutions for Mixed Fractions
- Example: ( 8\frac{3}{5} \div 3\frac{3}{4} ) → Convert to improper fractions, find reciprocal, multiply, and simplify.
- Always use cancellation where possible to simplify calculations.
Word Problems and Application
- Divide to solve problems about quantities (e.g., finding number of burgers, dosing medicine, filling containers).
- Convert answers as needed into whole numbers or mixed fractions.
True/False Review
- The denominator of any whole number is 1 (True).
- To find a reciprocal, swap numerator and denominator (True).
- You must change the division sign to multiplication when dividing fractions (True).
- Always simplify your answer (True).
- Get the reciprocal of the divisor before multiplying (True).
Key Terms & Definitions
- Fraction — A number representing part of a whole, written as numerator/denominator.
- Mixed Fraction — A whole number and a fraction combined (e.g., ( 2\frac{1}{3} )).
- Reciprocal — A fraction flipped upside down (numerator and denominator swapped).
- Improper Fraction — A fraction where the numerator is greater than or equal to the denominator.
- Quotient — The result of a division operation.
- Cancellation — Simplifying by dividing numerator and denominator by common factors.
Action Items / Next Steps
- Practice dividing given fractions and mixed numbers in your notebook.
- Complete learning tasks and solve the provided word problems.
- Review key rules and definitions to prepare for quizzes.