A flower garden has an area of $2 \frac{4}{5}$ $m^2$. Sunflowers are planted on $\frac{5}{6}$ of the flower garden. What is the area where the sunflowers are planted?

1. Problem Description

A flower garden has an area of $2 \frac{4}{5}$ $m^2$. Sunflowers are planted on $\frac{5}{6}$ of the flower garden. What is the area where the sunflowers are planted?

2. Solution Steps

First, convert the mixed number $2 \frac{4}{5}$ to an improper fraction.

$2 \frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{10+4}{5} = \frac{14}{5}$

Next, we need to find $\frac{5}{6}$ of $\frac{14}{5}$. This means we need to multiply the two fractions:

$\frac{14}{5} \times \frac{5}{6} = \frac{14 \times 5}{5 \times 6}$

We can simplify this fraction by canceling out the common factor of 5:

$\frac{14 \times 5}{5 \times 6} = \frac{14 \times 1}{1 \times 6} = \frac{14}{6}$

Now, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

$\frac{14}{6} = \frac{14 \div 2}{6 \div 2} = \frac{7}{3}$

Convert the improper fraction $\frac{7}{3}$ to a mixed number:

$\frac{7}{3} = 2 \frac{1}{3}$

The area where the sunflowers are planted is $\frac{14}{5} \times \frac{5}{6} = \frac{14 \times 5}{5 \times 6} = \frac{70}{30} = \frac{7}{3} m^2$

However, the image shows

$\frac{14}{5} \times \frac{6}{6} = \frac{14 \times 6}{5 \times 5} = \frac{84}{25}$.

Convert $\frac{84}{25}$ to mixed number. $84 = 3 \times 25 + 9$, so

$\frac{84}{25} = 3 \frac{9}{25}$. This does not equal $2 \frac{1}{3}$.

From the image,

$2 \frac{4}{5} \times \frac{5}{6} = \frac{14}{5} \times \frac{5}{6} = \frac{14 \times 5}{5 \times 6} = \frac{70}{30} = \frac{7}{3}$

$\frac{7}{3} = \frac{7 \times 5}{3 \times 5} = \frac{35}{15}$

The answer is $\frac{7}{3}$ which is $2 \frac{1}{3}$

or

$\frac{14 \times 6}{5 \times 6} = \frac{84}{25} = 3 \frac{9}{25}$. There is an error in the problem.

3. Final Answer

$\frac{7}{3}$ $m^2$ or $\frac{84}{25}$ $m^2$.

$\frac{84}{25} m^2$