Dividing fractions is easier than it seems! Instead of directly dividing, you simply multiply the first fraction by the reciprocal of the second fraction. The reciprocal is found by flipping the numerator and the denominator of the fraction.
The "Keep, Change, Flip" Method
A common and easy way to remember how to divide fractions is the "Keep, Change, Flip" method:
- 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).
Now you have a multiplication problem, which is much simpler to solve. Multiply the numerators together and then multiply the denominators together. Simplify the resulting fraction if possible.
Example
Let's divide ½ by ⅓:
- Keep: ½
- Change: ÷ becomes ×
- Flip: ⅓ becomes ³/₁
The problem becomes: ½ × ³/₁ = (1 × 3) / (2 × 1) = ³/₂ or 1 ½
Why Does This Work?
Dividing by a fraction is the same as multiplying by its reciprocal. This is because division is the inverse operation of multiplication. Think of it this way: dividing by ⅓ is the same as asking "how many ⅓'s are there in ½?". Multiplying by 3 (the reciprocal of ⅓) answers that question.
More Examples
- Example 1: ¾ ÷ ⅔ = ¾ × ⅔ = (3 × 2) / (4 × 3) = ⁶/₁₂ = ½
- Example 2: ⁵/₆ ÷ ⁵/₁₂ = ⁵/₆ × ¹²/₅ = (5 × 12) / (6 × 5) = ⁶⁰/₃₀ = 2
- Example 3: 2 (written as ²/₁) ÷ ¼ = ²/₁ × ⁴/₁ = (2 × 4) / (1 × 1) = ⁸/₁ = 8
Remember to always simplify your answer to its lowest terms. Using this method, you can confidently tackle any fraction division problem. Multiple online resources such as Math with Mr. J, Mashup Math, and others provide further visual and detailed explanations.
