To find the value of [tex]\(\frac{3}{4} \div \frac{1}{2}\)[/tex], we will follow these steps:
1. Rewrite the division problem as a multiplication problem. When dividing by a fraction, you multiply by the reciprocal of that fraction. The reciprocal of [tex]\(\frac{1}{2}\)[/tex] is [tex]\(\frac{2}{1}\)[/tex].
So, the division [tex]\(\frac{3}{4} \div \frac{1}{2}\)[/tex] can be rewritten as:
[tex]\[\frac{3}{4} \times \frac{2}{1}\][/tex]
2. Multiply the numerators together and the denominators together.
- The numerator is [tex]\(3 \times 2 = 6\)[/tex].
- The denominator is [tex]\(4 \times 1 = 4\)[/tex].
This gives us:
[tex]\[\frac{6}{4}\][/tex]
3. Simplify the fraction if possible. The fraction [tex]\(\frac{6}{4}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 6 and 4 is 2.
Simplifying [tex]\(\frac{6}{4}\)[/tex] by dividing both the numerator and the denominator by 2, we get:
[tex]\[\frac{6 \div 2}{4 \div 2} = \frac{3}{2}\][/tex]
4. Convert the improper fraction to a mixed number. The fraction [tex]\(\frac{3}{2}\)[/tex] can be written as a mixed number:
[tex]\[\frac{3}{2} = 1 \frac{1}{2}\][/tex]
So, the value of [tex]\(\frac{3}{4} \div \frac{1}{2}\)[/tex] is [tex]\(1 \frac{1}{2}\)[/tex].
Among the given choices, the correct answer is:
[tex]\[\boxed{1 \frac{1}{2}}\][/tex]
