Question

find the volume of the rectangular prism. write your answer in simplest form. the rectangular prism has dimensions: 2 m, \\(\frac{5}{6}\\) m, \\(\frac{5}{9}\\) m

Explanation:

Step1: Recuerda la fórmula del volumen de un prisma rectangular

El volumen \( V \) de un prisma rectangular se calcula como \( V = l \times w \times h \), donde \( l \) es la longitud, \( w \) es el ancho y \( h \) es la altura.
En este caso, \( l = 2 \, \text{m} \), \( w = \frac{5}{6} \, \text{m} \) y \( h = \frac{5}{9} \, \text{m} \).

Step2: Sustituye los valores en la fórmula

Sustituimos los valores en la fórmula: \( V = 2 \times \frac{5}{6} \times \frac{5}{9} \).

Step3: Realiza la multiplicación

Primero, multiplica \( 2 \) y \( \frac{5}{6} \): \( 2 \times \frac{5}{6} = \frac{10}{6} = \frac{5}{3} \).
Luego, multiplica \( \frac{5}{3} \) y \( \frac{5}{9} \): \( \frac{5}{3} \times \frac{5}{9} = \frac{25}{27} \)? Espera, no, espera. Wait, 2 es \( \frac{2}{1} \), entonces:

\( V = \frac{2}{1} \times \frac{5}{6} \times \frac{5}{9} \)

Simplifica \( \frac{2}{6} = \frac{1}{3} \), entonces:

\( V = \frac{1}{3} \times 5 \times \frac{5}{9} \)? No, mejor así:

\( 2 \times \frac{5}{6} = \frac{10}{6} = \frac{5}{3} \), luego \( \frac{5}{3} \times \frac{5}{9} = \frac{25}{27} \)? Wait, no, 25=10, 105=50; 16=6, 69=54. Entonces \( \frac{50}{54} = \frac{25}{27} \)? Wait, no, 2 es \( \frac{2}{1} \), así que:

\( \frac{2}{1} \times \frac{5}{6} \times \frac{5}{9} = \frac{2 \times 5 \times 5}{1 \times 6 \times 9} = \frac{50}{54} = \frac{25}{27} \)? Wait, no, 2 y 6 se simplifican: 2 ÷ 2 = 1, 6 ÷ 2 = 3. Entonces:

\( \frac{1}{1} \times \frac{5}{3} \times \frac{5}{9} = \frac{25}{27} \)? Wait, no, 25=10, 105=50; 16=6, 69=54. 50 y 54 se dividen por 2: 25/27. Sí, eso es correcto.

Wait, pero 2 metros, \( \frac{5}{6} \) metros y \( \frac{5}{9} \) metros. Entonces:

\( V = 2 \times \frac{5}{6} \times \frac{5}{9} \)

Calcula paso a paso:

2 * 5/6 = 10/6 = 5/3

Luego, 5/3 5/9 = 25/27? Wait, no, 55=25, 3*9=27. Sí. Entonces el volumen es \( \frac{25}{27} \) metros cúbicos? Wait, no, wait, 2 es 2/1, así que:

2/1 5/6 = (25)/(1*6) = 10/6 = 5/3

Then 5/3 * 5/9 = 25/27. Yes.

Wait, but let's check again. The dimensions are 2 m, 5/6 m, and 5/9 m. So volume is length × width × height. So:

\( V = 2 \times \frac{5}{6} \times \frac{5}{9} \)

Multiply the numerators: 2 × 5 × 5 = 50

Multiply the denominators: 1 × 6 × 9 = 54

Simplify 50/54 by dividing numerator and denominator by 2: 25/27. So the volume is 25/27 cubic meters? Wait, but that seems small. Wait, 5/6 is about 0.833, 5/9 is about 0.555, 20.833=1.666, 1.6660.555≈0.925, and 25/27≈0.925. Yes, that's correct.

Wait, but maybe I made a mistake. Let's do it again:

\( V = l \times w \times h = 2 \times \frac{5}{6} \times \frac{5}{9} \)

First, multiply 2 and 5/6:

2 5/6 = (25)/6 = 10/6 = 5/3

Then multiply 5/3 and 5/9:

(55)/(39) = 25/27

Yes, that's correct. So the volume is 25/27 cubic meters? Wait, but the problem says "write your answer in simplest form". So 25/27 is already in simplest form because 25 and 27 have no common factors other than 1 (25 is 5², 27 is 3³). So that's the answer.

Answer:

\(\frac{25}{27}\)