Division of Mixed Numbers
Learn how to divide mixed numbers using the powerful Keep-Change-Flip method!
What is Dividing Mixed Numbers?
- Finding how many times one mixed number fits into another
- Splitting a mixed number into equal parts
- The inverse operation of multiplication
- Example: 3¾ ÷ 1½ asks "How many 1½s are in 3¾?"
Key Principle: Convert mixed numbers to improper fractions first, then use "multiply by reciprocal"!
What is a Reciprocal?
A reciprocal is a fraction "flipped" — the numerator and denominator switch places!
| Number | As Improper Fraction | Reciprocal |
|---|---|---|
| 2½ | 5/2 | 2/5 |
| 1¾ | 7/4 | 4/7 |
| 3 | 3/1 | 1/3 |
Magic Property: Number × Reciprocal = 1
Example: 5/2 × 2/5 = 10/10 = 1
Example: 5/2 × 2/5 = 10/10 = 1
THE GOLDEN RULE: Keep-Change-Flip
KEEP
Keep the first fraction exactly as it is
CHANGE
Change the division sign (÷) to multiplication (×)
FLIP
Flip the second fraction (take its reciprocal)