Dividing a big number by a fraction involves multiplying the big number by the fraction's reciprocal. This process is straightforward and ensures accurate calculations.
Understanding the Reciprocal
The reciprocal of a fraction is found by swapping its numerator and denominator. For example, the reciprocal of 2/3 is 3/2. Understanding this concept is crucial for dividing by a fraction.
Steps to Divide a Big Number by a Fraction
- Identify the big number and the fraction. Let's take 100 as the big number and 3/4 as the fraction.
- Find the reciprocal of the fraction. The reciprocal of 3/4 is 4/3.
- Multiply the big number by the reciprocal. In our example, multiply 100 by 4/3, which is 100 * (4/3).
- Calculate the result. 100 * (4/3) = 400/3.
- Simplify if necessary. 400/3 can be expressed as a mixed number, which is 133 1/3 or as a decimal approximation.
Examples
Here are a few more examples:
- Example 1: Divide 50 by 1/2
- Reciprocal of 1/2 is 2/1.
- 50 * 2/1 = 100
- Example 2: Divide 150 by 2/5
- Reciprocal of 2/5 is 5/2
- 150 * 5/2 = 750/2 = 375
- Example 3: Divide 250 by 5/6
- Reciprocal of 5/6 is 6/5
- 250 * 6/5 = 1500/5 = 300
Practical Insights
- Dividing by a fraction is essentially the same as asking how many times the fraction can fit into the big number.
- This method works with any fraction, regardless of its size or value.
- The result can be a whole number, a fraction, or a mixed number, depending on the division.
Table Summary
| Operation | Original Fraction | Reciprocal of Fraction | Calculation | Result |
|---|---|---|---|---|
| 100 ÷ 3/4 | 3/4 | 4/3 | 100 * 4/3 | 400/3 |
| 50 ÷ 1/2 | 1/2 | 2/1 | 50 * 2/1 | 100 |
| 150 ÷ 2/5 | 2/5 | 5/2 | 150 * 5/2 | 375 |
| 250 ÷ 5/6 | 5/6 | 6/5 | 250 * 6/5 | 300 |
Conclusion
Dividing a big number by a fraction is achieved by multiplying the number by the reciprocal of the fraction. This approach provides a simple and effective way to perform division involving fractions. The key step is to flip the fraction and then multiply.
