Dividing fractions is straightforward: multiply the first fraction by the reciprocal (flipped version) of the second fraction.
Here's a breakdown of the process:
Understanding Reciprocals
The reciprocal of a fraction is obtained by swapping its numerator (top number) and its denominator (bottom number).
- Example: The reciprocal of 2/3 is 3/2. The reciprocal of 5 (which can be written as 5/1) is 1/5.
The Division Process: "Keep, Change, Flip"
The rule of thumb for dividing fractions is often remembered as "Keep, Change, Flip":
- Keep: Keep the first fraction exactly as it is.
- Change: Change the division sign (÷) to a multiplication sign (×).
- Flip: Flip the second fraction (find its reciprocal).
Performing the Multiplication
Once you've "kept, changed, and flipped," you simply multiply the two fractions together. To multiply fractions:
- Multiply the numerators (top numbers) together.
- Multiply the denominators (bottom numbers) together.
- Simplify the resulting fraction, if possible.
Example
Let's say you want to divide 1/2 by 3/4:
- Keep: 1/2
- Change: ÷ to ×
- Flip: 3/4 becomes 4/3
Now, multiply:
(1/2) × (4/3) = (1 × 4) / (2 × 3) = 4/6
Finally, simplify the fraction 4/6. Both 4 and 6 are divisible by 2:
4/6 = 2/3
Therefore, (1/2) ÷ (3/4) = 2/3
Dividing Mixed Numbers
If you need to divide mixed numbers (e.g., 1 1/2), first convert them into improper fractions:
- Multiply the whole number by the denominator of the fractional part.
- Add the numerator of the fractional part to the result.
- Place the sum over the original denominator.
Example: Convert 1 1/2 to an improper fraction:
- 1 × 2 = 2
- 2 + 1 = 3
- Improper fraction: 3/2
Then, proceed with the "Keep, Change, Flip" method as described above.
Summary
Dividing fractions involves multiplying the first fraction by the reciprocal of the second. This "Keep, Change, Flip" method simplifies the division process into a multiplication problem. Remember to convert mixed numbers to improper fractions before dividing.
