Dividing fractions involves a simple yet crucial technique: keep, change, and flip. This method transforms a division problem into a multiplication problem, making it easy to solve.
Understanding the Keep, Change, Flip Method
The core concept is that dividing by a fraction is the same as multiplying by its reciprocal. The "keep, change, flip" process simplifies this concept. Let's break it down:
- Keep: You retain the first fraction exactly as it is.
- Change: You transform the division sign (÷) into a multiplication sign (×).
- Flip: You take the second fraction and flip it, creating its reciprocal. This means switching the numerator and the denominator.
Step-by-Step Guide with an Example
Let’s illustrate how to divide fractions with an example:
Suppose we want to divide 2/3 by 1/4.
- Keep the first fraction: 2/3 remains 2/3.
- Change the division sign to a multiplication sign: ÷ becomes ×.
- Flip the second fraction (1/4 becomes 4/1): 1/4 becomes 4/1.
Now we have a multiplication problem: 2/3 × 4/1.
Solving the Multiplication Problem
- Multiply the numerators: 2 × 4 = 8
- Multiply the denominators: 3 × 1 = 3
The result is 8/3.
Therefore, 2/3 divided by 1/4 is 8/3. This can also be expressed as the mixed number 2 2/3.
Additional Insights and Tips
- Reciprocal: Remember that the reciprocal of a fraction is found by inverting it. For example, the reciprocal of 5/7 is 7/5.
- Whole Numbers: If you're dividing a fraction by a whole number, treat the whole number as a fraction with a denominator of 1 (e.g., 5 = 5/1).
- Mixed Numbers: Before dividing, convert any mixed numbers into improper fractions.
Summary
Dividing fractions is simplified by using the "keep, change, flip" method, which transforms the division into an easily solvable multiplication problem using reciprocals.
