Calculating 1 1/2 divided by 3 transforms a simple arithmetic problem into a practical demonstration of fraction manipulation. Understanding how to divide a mixed number by a whole number is a fundamental skill with applications ranging from cooking measurements to financial planning. This process relies on converting the mixed number into an improper fraction to simplify the operation and ensure accuracy.
Converting the Mixed Number to an Improper Fraction
The first step in solving 1 1/2 divided by 3 is to address the mixed number, 1 1/2. A mixed number combines a whole number with a fraction, but dividing it directly is inefficient. We must convert it into an improper fraction, where the numerator is larger than the denominator.
To perform this conversion, multiply the whole number (1) by the denominator of the fraction (2), which equals 2. Add the numerator (1) to this result, yielding 3. This sum becomes the new numerator, while the denominator (2) remains unchanged. Consequently, 1 1/2 is equivalent to the improper fraction 3/2.
Expressing the Division as a Single Fraction
With the mixed number converted, the problem becomes 3/2 divided by 3. To maintain clarity, it is helpful to express the whole number 3 as a fraction. Any whole number can be written as itself divided by 1, so 3 becomes 3/1.
The division problem is now represented as 3/2 ÷ 3/1. This format makes the mathematical rule for dividing fractions immediately apparent and prepares us to apply the standard algorithmic approach.
Applying the Reciprocal Rule
The core principle of dividing fractions is to multiply by the reciprocal of the divisor. The divisor is the number by which you are dividing, which in this case is 3/1. The reciprocal of a fraction is created by swapping its numerator and denominator.
The reciprocal of 3/1 is 1/3. By changing the division sign to multiplication and using this reciprocal, the problem is transformed. The expression 3/2 ÷ 3/1 becomes 3/2 × 1/3.
Multiplying the Fractions
Multiplying the fractions involves a straightforward process. Multiply the numerators together and the denominators together.
- Numerator: 3 × 1 = 3
- Denominator: 2 × 3 = 6
This yields the fraction 3/6.
Simplifying to the Final Answer
The final step is to simplify 3/6 to its lowest terms. Both the numerator and the denominator share a common factor of 3.
Dividing both by 3 results in 1/2. Therefore, the result of 1 1/2 divided by 3 is precisely 1/2.
| Step | Operation | Result |
|---|---|---|
| 1 | Convert 1 1/2 to an improper fraction | 3/2 |
| 2 | Rewrite 3 as a fraction (3/1) and apply reciprocal | 3/2 × 1/3 |
| 3 | Multiply numerators and denominators | 3/6 |
| 4 | Simplify the fraction | 1/2 |
