Question

find the value of the expression
\\( 3 \frac{3}{4} \div s \\)
for \\( s = 2 \frac{1}{2} \\).
write your answer as a fraction or as a whole or mixed number.

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(3\frac{3}{4}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(3\frac{3}{4}\), we have \(a = 3\), \(b = 3\), \(c = 4\). Then \(3\frac{3}{4}=\frac{3\times4 + 3}{4}=\frac{12 + 3}{4}=\frac{15}{4}\).

Next, convert \(2\frac{1}{2}\) to an improper fraction. Using the same formula, \(a = 2\), \(b = 1\), \(c = 2\). So \(2\frac{1}{2}=\frac{2\times2+1}{2}=\frac{4 + 1}{2}=\frac{5}{2}\).

Step2: Substitute the value of \(s\) into the expression and perform the division

The expression is \(3\frac{3}{4}\div s\), and \(s = 2\frac{1}{2}=\frac{5}{2}\). So we have \(\frac{15}{4}\div\frac{5}{2}\).

When dividing fractions, we multiply by the reciprocal of the divisor. The reciprocal of \(\frac{5}{2}\) is \(\frac{2}{5}\). So \(\frac{15}{4}\div\frac{5}{2}=\frac{15}{4}\times\frac{2}{5}\).

Step3: Simplify the multiplication

Multiply the numerators and denominators: \(15\times2 = 30\) and \(4\times5 = 20\). So we have \(\frac{30}{20}\).

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 10. \(\frac{30\div10}{20\div10}=\frac{3}{2}\).

Convert \(\frac{3}{2}\) to a mixed number: \(\frac{3}{2}=1\frac{1}{2}\).

Answer:

\(1\frac{1}{2}\)