To solve the problem [tex]\(\frac{1}{2} \div \frac{2}{3}\)[/tex], let me explain the step-by-step process.
Dividing fractions typically involves using the reciprocal (or "invert and multiply") method rather than the "divide by one" strategy. Here's how you can solve the problem:
1. Understand the problem: You need to divide [tex]\(\frac{1}{2}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex].
2. Reciprocal method: Since dividing by a fraction is the same as multiplying by its reciprocal, we need to find the reciprocal of [tex]\(\frac{2}{3}\)[/tex].
- The reciprocal of [tex]\(\frac{2}{3}\)[/tex] is [tex]\(\frac{3}{2}\)[/tex].
3. Rewrite the division as a multiplication: Replace the division with multiplication by the reciprocal of [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
\frac{1}{2} \div \frac{2}{3} = \frac{1}{2} \times \frac{3}{2}
\][/tex]
4. Multiply the fractions: To multiply the fractions, multiply the numerators together and the denominators together:
[tex]\[
\frac{1}{2} \times \frac{3}{2} = \frac{1 \times 3}{2 \times 2} = \frac{3}{4}
\][/tex]
5. Simplify the result: The resulting fraction [tex]\(\frac{3}{4}\)[/tex] is already in its simplest form.
Therefore, the result of dividing [tex]\(\frac{1}{2}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex] is [tex]\(\frac{3}{4}\)[/tex], which as a decimal is 0.75.
So, to answer your original question, the "divide by one" strategy does not directly apply to this problem. Instead, you use the reciprocal method to divide fractions effectively. The final result is [tex]\(\frac{3}{4}\)[/tex] or 0.75.
