Overview
This lecture explains how to divide a fraction by another fraction using the "keep, switch, flip" (multiply by the reciprocal) method, with two example problems.
Steps for Dividing Fractions
- To divide a fraction by a fraction, follow the steps: keep, switch, flip.
- Keep the first fraction as it is.
- Switch the operation from division to multiplication.
- Flip the second fraction to get its reciprocal (swap numerator and denominator).
- Multiply the resulting 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 to multiplication, flip 1/7 to 7/1.
- Multiply: 3 × 7 = 21, 4 × 1 = 4, so result is 21/4.
- Convert 21/4 to mixed number: 5 and 1/4.
Example 2: 2/3 ÷ 2/5
- Keep 2/3.
- Switch to multiplication, flip 2/5 to 5/2.
- Multiply: 2 × 5 = 10, 3 × 2 = 6, so result is 10/6.
- Convert 10/6 to mixed number: 1 and 4/6.
- Simplify 4/6 to 2/3, so final answer is 1 and 2/3.
Key Terms & Definitions
- Reciprocal — A fraction flipped so the numerator becomes the denominator and vice versa.
- Improper Fraction — A fraction where the numerator is greater than or equal to the denominator.
- Mixed Number — A number made up of a whole number and a proper fraction.
- Simplify — Reducing a fraction to its lowest terms.
Action Items / Next Steps
- Practice dividing fractions using the "keep, switch, flip" method.
- Convert answers to mixed numbers and simplify fractions as needed.