Question

a cooperative garden owns $19\\ 3/5$ acres of fertile land. the plot will be divided equally among 12 members. how many acres will each member receive?
$1\\ 9/30$ acres
2 acres
$1\\ 3/5$ acres
$1\\ 19/30$ acres

Explanation:

Step1: Convert mixed number to improper fraction

The total land is \(19\frac{3}{5}\) acres. To convert the mixed number to an improper fraction, we use the formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So, \(19\frac{3}{5}=\frac{19\times5 + 3}{5}=\frac{95+3}{5}=\frac{98}{5}\) acres.

Step2: Divide the total land by the number of members

We need to divide \(\frac{98}{5}\) acres by 12 members. Dividing by a number is the same as multiplying by its reciprocal, so \(\frac{98}{5}\div12=\frac{98}{5}\times\frac{1}{12}\).

Step3: Simplify the fraction

Multiply the numerators and denominators: \(\frac{98\times1}{5\times12}=\frac{98}{60}\). Simplify this fraction by dividing both the numerator and denominator by 2: \(\frac{98\div2}{60\div2}=\frac{49}{30}\).

Step4: Convert improper fraction to mixed number

Now, convert \(\frac{49}{30}\) to a mixed number. Divide 49 by 30: \(49\div30 = 1\) with a remainder of \(19\). So, \(\frac{49}{30}=1\frac{19}{30}\) acres.

Answer:

1 19/30 acres