Overview
This lesson explains step-by-step methods for multiplying and dividing mixed numbers, including converting between mixed and improper fractions and simplifying results.
Multiplying Mixed Numbers
- Convert mixed numbers to improper fractions before multiplying.
- To convert, multiply denominator by whole number and add numerator (e.g., (2\frac{1}{3} = \frac{7}{3})).
- Simplify fractions if possible by canceling common factors.
- Multiply numerators together and denominators together.
- Convert the resulting improper fraction back to a mixed number by dividing numerator by denominator.
Multiplication Examples
- (2\frac{1}{3} \times 1\frac{3}{4} = \frac{7}{3} \times \frac{7}{4} = \frac{49}{12} = 4\frac{1}{12})
- (6\frac{2}{3} \times \frac{1}{4} = \frac{20}{3} \times \frac{1}{4} = \frac{5}{3} = 1\frac{2}{3})
- (8 \times 2\frac{5}{6} = \frac{8}{1} \times \frac{17}{6} = \frac{68}{3} = 22\frac{2}{3})
Dividing Mixed Numbers
- Convert all mixed numbers to improper fractions.
- Rewrite the division as multiplication by the reciprocal of the divisor (second fraction).
- Only the second fraction is flipped when finding the reciprocal.
- Simplify before multiplying if possible.
- Multiply and then convert the answer back to a mixed number.
Division Examples
- (10 \div 3\frac{1}{5} = \frac{10}{1} \div \frac{16}{5} = \frac{10}{1} \times \frac{5}{16} = \frac{25}{8} = 3\frac{1}{8})
- (1\frac{7}{8} \div 1\frac{2}{3} = \frac{15}{8} \div \frac{5}{3} = \frac{15}{8} \times \frac{3}{5} = \frac{9}{8} = 1\frac{1}{8})
Key Terms & Definitions
- Mixed Number — A number with a whole part and a fractional part (e.g., (2\frac{1}{3})).
- Improper Fraction — A fraction where the numerator is greater than or equal to the denominator (e.g., (\frac{7}{3})).
- Reciprocal — The inverse of a fraction, obtained by swapping numerator and denominator.
Action Items / Next Steps
- Practice multiplying and dividing mixed numbers, converting between mixed numbers and improper fractions.
- Complete any assigned homework problems on this topic.