Question

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Explanation:

Step1: Convert mixed number to improper fraction

The total paint is \( 6\frac{3}{4} \) gallons. To convert the mixed number to an improper fraction, we use the formula \( a\frac{b}{c}=\frac{a\times c + b}{c} \). So for \( 6\frac{3}{4} \), we have \( \frac{6\times4 + 3}{4}=\frac{24 + 3}{4}=\frac{27}{4} \) gallons.

Step2: Divide total paint by container capacity

We need to find how many times \( \frac{3}{5} \) gallon fits into \( \frac{27}{4} \) gallons. This is a division of fractions: \( \frac{27}{4}\div\frac{3}{5} \). When dividing fractions, we multiply by the reciprocal, so \( \frac{27}{4}\times\frac{5}{3} \).

Step3: Simplify and multiply

Simplify \( \frac{27}{4}\times\frac{5}{3} \). The 27 and 3 can be simplified: \( 27\div3 = 9 \), \( 3\div3 = 1 \). So we get \( \frac{9}{4}\times\frac{5}{1}=\frac{45}{4}=11.25 \). Since we need the number of full containers, we take the integer part, which is 11.

Answer:

11