Question

d -45/60 (12 15/24

Explanation:

Step1: Simplify the fraction \(\frac{-45}{60}\)

First, find the greatest common divisor (GCD) of 45 and 60. The GCD of 45 and 60 is 15. Divide both the numerator and the denominator by 15: \(\frac{-45\div15}{60\div15}=\frac{-3}{4}\)

Step2: Simplify the mixed number \(12\frac{15}{24}\)

Simplify the fractional part \(\frac{15}{24}\). The GCD of 15 and 24 is 3. Divide both by 3: \(\frac{15\div3}{24\div3}=\frac{5}{8}\). So \(12\frac{15}{24}=12\frac{5}{8}\). Convert this mixed number to an improper fraction: \(12\frac{5}{8}=\frac{12\times8 + 5}{8}=\frac{96+5}{8}=\frac{101}{8}\)

Step3: Multiply the two simplified fractions

Now we have \(\frac{-3}{4}\times\frac{101}{8}\). Multiply the numerators and the denominators: \(\frac{-3\times101}{4\times8}=\frac{-303}{32}\)

Step4: Convert back to a mixed number (optional, but for clarity)

Divide -303 by 32: \(32\times(-9)= -288\), and \(-303-(-288)=-15\). So \(\frac{-303}{32}=-9\frac{15}{32}\)

Answer:

\(-9\frac{15}{32}\) (or \(\frac{-303}{32}\))