Question

problem 8 determine the quotient of $33.8 \div 32.5$.

Explanation:

Step1: Convert decimals to fractions

We can write \(33.8\) as \(\frac{338}{10}\) and \(32.5\) as \(\frac{325}{10}\). So the division \(33.8\div32.5\) becomes \(\frac{338}{10}\div\frac{325}{10}\).

Step2: Divide the fractions

When dividing fractions, we multiply by the reciprocal. So \(\frac{338}{10}\times\frac{10}{325}\). The \(10\) in the numerator and denominator cancels out, leaving \(\frac{338}{325}\).

Step3: Simplify the fraction

We can divide both the numerator and the denominator by \(13\). \(338\div13 = 26\) and \(325\div13=25\). So \(\frac{338}{325}=\frac{26}{25}\).

Step4: Convert to decimal

\(\frac{26}{25}=26\div25 = 1.04\).

Answer:

\(1.04\)