Overview
This lecture explains how to divide a fraction by another fraction using the "keep, switch, flip" method, with detailed examples and important steps.
Steps to Divide Fractions (Keep, Switch, Flip)
- Keep the first fraction as it is.
- Switch the division sign to multiplication.
- Flip the second fraction (write its reciprocal; numerator and denominator switch places).
- Multiply the two fractions straight across (numerators together, denominators together).
- If the result is an improper fraction, convert it to a mixed number.
- Simplify the fractional part of the mixed number if possible.
Example 1: 3/4 ÷ 1/7
- Keep: 3/4
- Switch: Change division to multiplication.
- Flip: 1/7 becomes 7/1.
- Multiply: 3 × 7 = 21; 4 × 1 = 4; result is 21/4.
- Convert 21/4 to a mixed number: 5 and 1/4.
- Final answer: 3/4 ÷ 1/7 = 5 and 1/4.
Example 2: 2/3 ÷ 2/5
- Keep: 2/3
- Switch: Change division to multiplication.
- Flip: 2/5 becomes 5/2.
- Multiply: 2 × 5 = 10; 3 × 2 = 6; result is 10/6.
- Convert 10/6 to a mixed number: 1 and 4/6.
- Simplify 4/6 to 2/3.
- Final answer: 2/3 ÷ 2/5 = 1 and 2/3.
Key Terms & Definitions
- Reciprocal — A fraction flipped upside down (numerator and denominator switch places).
- Improper fraction — A fraction where the numerator is greater than or equal to the denominator.
- Mixed number — A number with a whole part and a fractional part.
Action Items / Next Steps
- Practice dividing more fractions using the keep, switch, flip method.
- Check if results can be simplified or need to be written as mixed numbers.