Overview
This lecture covers how to divide simple fractions and mixed fractions by using reciprocals and converting division problems into multiplication, including several examples and practice problems.
Dividing Simple Fractions
- To divide fractions, multiply the first fraction by the reciprocal of the second fraction (the divisor).
- The reciprocal is found by swapping the numerator and denominator.
- Write all numbers as fractions before dividing.
- Always simplify the final answer to its lowest terms.
Steps for Dividing Fractions
- Rewrite the division as multiplication.
- Take the reciprocal of the divisor (second fraction only).
- Cancel common factors in numerators and denominators if possible.
- Multiply numerators together and denominators together.
- Convert improper fractions to mixed numbers when needed.
Examples with Solutions
- Example: ( \frac{8}{9} \div \frac{2}{3} = \frac{8}{9} \times \frac{3}{2} = \frac{4}{3} ) (which simplifies to ( 1 \frac{1}{3} )).
- Practice problems involve similar steps, including cancellation, multiplication, and final simplification.
Dividing Mixed Numbers
- Convert mixed numbers to improper fractions.
- Follow the same steps as for simple fractions: reciprocal, multiply, simplify.
- Example: ( 8 \frac{3}{5} \div 3 \frac{3}{4} ) becomes ( \frac{43}{5} \div \frac{15}{4} = \frac{43}{5} \times \frac{4}{15} = \frac{172}{75} = 2 \frac{22}{75} ).
Word Problems & Application
- Convert quantities to fractions or mixed numbers as needed.
- Set up division problems based on scenario data.
- Solve using the dividing fractions method, then interpret the result.
True or False Concept Check
- Reciprocals swap numerator and denominator.
- The denominator of a whole number is one.
- Always change division to multiplication when dividing by a fraction.
- Always write answers in simplest form.
- Find the reciprocal only for the divisor.
- Check answers with sample calculations as given.
Key Terms & Definitions
- Reciprocal — A fraction flipped upside-down (numerator and denominator are interchanged).
- Divisor — The number or fraction that divides another.
- Dividend — The number or fraction to be divided.
- Improper fraction — A fraction with a numerator greater than or equal to the denominator.
- Mixed number — A whole number combined with a fraction.
Action Items / Next Steps
- Complete the learning tasks and practice problems in your notebook.
- Review the process of converting mixed numbers to improper fractions and vice versa.
- Ensure all answers are in their simplest form.