Overview
This lecture explains how to divide a fraction by a fraction using the "keep, switch, flip" rule and demonstrates with step-by-step examples.
Steps for Dividing Fractions
- Use the "keep, switch, flip" method: keep the first fraction, switch division to multiplication, and flip the second fraction (find its reciprocal).
- After applying these steps, multiply the resulting fractions straight across (numerator to numerator, denominator to denominator).
Example 1: 3/4 ÷ 1/7
- Keep 3/4, switch division to multiplication, flip 1/7 to 7/1.
- Multiply: 3 × 7 = 21, 4 × 1 = 4, so the answer is 21/4.
- Convert 21/4 to a mixed number: 21 ÷ 4 = 5 with a remainder of 1, so the answer is 5 1/4.
- Check if the fractional part (1/4) can be simplified; in this case, it is already in simplest form.
Example 2: 2/3 ÷ 2/5
- Keep 2/3, switch division to multiplication, flip 2/5 to 5/2.
- Multiply: 2 × 5 = 10, 3 × 2 = 6, so the answer is 10/6.
- Convert 10/6 to a mixed number: 10 ÷ 6 = 1 with a remainder of 4, so the answer is 1 4/6.
- Simplify 4/6 to 2/3, so the final answer is 1 2/3.
Key Terms & Definitions
- Reciprocal — A fraction flipped upside down; numerator and denominator are switched.
- Improper fraction — A fraction where the numerator is larger than or equal to the denominator.
- Mixed number — A number consisting of a whole number and a fraction.
- Simplest form — A fraction where the numerator and denominator have no common factors except 1.
Action Items / Next Steps
- Practice dividing fractions by fractions using the "keep, switch, flip" method.
- Convert improper fractions to mixed numbers and simplify when possible.