Question

a recipe calls for \\(\frac{1}{3}\\) liters of water for every \\(\frac{3}{4}\\) kg of flour. how much water is needed for one kg of flour?

Explanation:

Step1: Define the ratio

We know that for $\frac{3}{4}$ kg of flour, we need $\frac{1}{3}$ liters of water. Let $x$ be the liters of water needed for 1 kg of flour. The ratio of water to flour should be constant. So we can set up a proportion: $\frac{\frac{1}{3}}{\frac{3}{4}}=\frac{x}{1}$.

Step2: Solve the proportion

To solve for $x$, we can use cross - multiplication. First, simplify $\frac{\frac{1}{3}}{\frac{3}{4}}$. Dividing by a fraction is the same as multiplying by its reciprocal, so $\frac{1}{3}\div\frac{3}{4}=\frac{1}{3}\times\frac{4}{3}=\frac{4}{9}$. Then, from the proportion $\frac{4}{9}=\frac{x}{1}$, we can see that $x = \frac{4}{9}$.

Answer:

$\frac{4}{9}$ liters