Question

Jacob used 1/7 of a liter of water to fill 1/9 of the fish aquarium. How many liters r needed to fill the aquarium?

Answer 1

We know that 1/7 of a liter filled up 1/9 of the aquarium, well, a "whole" will be 9/9.

how many liters will it be to fill up the 9/9 of the aquarium?

$\bf \begin{array}{ccll} \stackrel{liters}{water}&\stackrel{fish}{aquarium}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{1}{7}&\frac{1}{9}\\\\ w&\frac{9}{9} \end{array}\implies \cfrac{\frac{1}{7}}{w}=\cfrac{\frac{1}{9}}{\frac{9}{9}}\implies \cfrac{\frac{1}{7}}{\frac{w}{1}}=\cfrac{\frac{1}{9}}{\frac{9}{9}}\implies \cfrac{1}{7}\cdot \cfrac{1}{w}=\cfrac{1}{9}\cdot \cfrac{9}{9} \\\\\\ \cfrac{1}{7w}=\cfrac{1}{9}\implies 9=7w\implies \cfrac{9}{7}=w$

Answer 2

Since 1/7 L of water fills 1/9 of the aquarium, 9 times 1/7 will fill the aquarium:

9(1/7) = 9/7 = 1 2/7 L of water will fill the aquarium.