Definition: To divide by a fraction, multiply by its reciprocal: a/b divided by c/d equals a/b times d/c.
How do you divide by a fraction?
Keep the first number, change division to multiplication, and flip the second fraction. This is often called keep, change, flip.
Why does it work?
Dividing asks how many groups fit. How many 1/4s fit in 3? Each whole holds 4 fourths, so 3 holds 12. That equals 3 x 4/1.
What does a worked example look like?
Compute 5/6 divided by 2/9.
- Flip the divisor: 2/9 becomes 9/2.
- Multiply: 5/6 x 9/2 = 45/12.
- Simplify by dividing by 3: 15/4, or 3 3/4.
Check by estimating: 5/6 is almost 1 and 2/9 is a bit over 1/5, so the answer should be a bit under 5. That fits.
Which mistake is common?
Flipping the wrong fraction. Only the divisor, the second fraction, is inverted. Another trap is forgetting to convert mixed numbers to improper fractions first.
Where to learn it
Related terms
How to divide by a fraction
To divide by a fraction, there is one move: keep the first fraction, change division to multiplication, and flip the second fraction. For example, 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8. Write whole numbers and mixed numbers as fractions before you divide: 2 ÷ 1/3 = 2/1 × 3/1 = 6, which shows that 1/3 fits into 2 six times. Simplify at the end, or cross-cancel before you multiply. Dividing by a fraction less than 1 makes the result larger than the number you started with.