To solve the problem [tex]\(\frac{3}{4} \div \frac{3}{10}\)[/tex], follow these steps:
1. Understand dividing fractions: When you divide fractions, you multiply by the reciprocal of the divisor. The given expression [tex]\(\frac{3}{4} \div \frac{3}{10}\)[/tex] can be rewritten using multiplication:
[tex]\[
\frac{3}{4} \div \frac{3}{10} = \frac{3}{4} \times \frac{10}{3}
\][/tex]
2. Multiply the fractions: Multiply the numerators and the denominators:
[tex]\[
\frac{3}{4} \times \frac{10}{3} = \frac{3 \times 10}{4 \times 3} = \frac{30}{12}
\][/tex]
3. Simplify the fraction: To simplify [tex]\(\frac{30}{12}\)[/tex], find the greatest common divisor (GCD) of 30 and 12. The GCD is 6. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{30 \div 6}{12 \div 6} = \frac{5}{2}
\][/tex]
4. Convert to a mixed number: Since [tex]\(\frac{5}{2}\)[/tex] is an improper fraction, convert it to a mixed number:
- Divide the numerator by the denominator: [tex]\(5 \div 2 = 2\)[/tex] with a remainder of 1.
- So, [tex]\( \frac{5}{2} = 2 \frac{1}{2} \)[/tex].
Thus, the answer is:
[tex]\[ 2 \frac{1}{2} \][/tex]
Among the provided choices, [tex]\(2 \frac{1}{2}\)[/tex] is the correct answer.
