Brian irons (2)/(9) of his shirt in 3(3)/(5) minutes. Brian irons at a constant rate. At this rate, how much of his shirt does he iron each minute? of his shirt

Identify total amount and time: Identify the total amount of the shirt ironed and the total time taken. Brian irons 2/9 of his shirt in 3 3/5 minutes. Convert the mixed number to an improper fraction for easier calculation. 3 3/5 = (3*5 + 3)/5 = (15 + 3)/5 = 18/5 minutes.Convert mixed number: Calculate the rate at which Brian irons his shirt per minute. The rate is the amount of shirt ironed divided by the time taken. Rate = (Amount of shirt ironed) / (Time taken) Rate = (2/9) / (18/5)Calculate rate per minute: Perform the division to find the rate per minute. Rate = (2/9) * (5/18) (Since dividing by a fraction is the same as multiplying by its reciprocal) Rate = (2*5) / (9*18) Rate = 10 / 162Perform division: Simplify the fraction to its lowest terms. 10 and 162 have a common factor of 2. Rate = (10/2) / (162/2) Rate = 5 / 81

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Q. Brian irons

\frac{2}{9}

of his shirt in

3 \frac{3}{5}

minutes. Brian irons at a constant rate.

\newline

At this rate, how much of his shirt does he iron each minute?

\newline

of his shirt

Identify total amount and time: Identify the total amount of the shirt ironed and the total time taken. $\newline$ Brian irons $\frac{2}{9}$ of his shirt in $3\,\frac{3}{5}$ minutes. $\newline$ Convert the mixed number to an improper fraction for easier calculation. $\newline$ $3\,\frac{3}{5} = \frac{(3\times5 + 3)}{5} = \frac{(15 + 3)}{5} = \frac{18}{5}$ minutes.
Substitute the Values in the Rate Formula: Calculate the rate at which Brian irons his shirt per minute. $\newline$ The rate is the amount of shirt ironed divided by the time taken. $\newline$ Rate = $\frac{\text{Amount of shirt ironed}}{\text{Time taken}}$ $\newline$ Rate = $\frac{\frac{2}{9}}{\frac{18}{5}}$
Calculate rate per minute: Perform the division to find the rate per minute. $\newline$ Rate = $(\frac{2}{9}) \times (\frac{5}{18})$ (Since dividing by a fraction is the same as multiplying by its reciprocal) $\newline$ Rate = $\frac{(2\times5)}{(9\times18)}$ $\newline$ Rate = $\frac{10}{162}$
Perform division: Simplify the fraction to its lowest terms. $\newline$ $10$ and $162$ have a common factor of $2$ . $\newline$ Rate = $\frac{5}{81}$