Question

12/15 ratios and proportions
a farm yields \\(\frac{4}{5}\\) tons of wheat from \\(\frac{2}{3}\\) acres. what is the yield from one acre?

Explanation:

Step1: Understand the problem

We need to find the yield per acre. Yield per acre is total yield divided by total acres. So we divide $\frac{4}{5}$ tons by $\frac{2}{3}$ acres.

Step2: Divide the fractions

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. So $\frac{4}{5} \div \frac{2}{3} = \frac{4}{5} \times \frac{3}{2}$.

Step3: Multiply the numerators and denominators

Multiply the numerators: $4\times3 = 12$. Multiply the denominators: $5\times2 = 10$. So we get $\frac{12}{10}$.

Step4: Simplify the fraction

Simplify $\frac{12}{10}$ by dividing numerator and denominator by 2. $\frac{12\div2}{10\div2} = \frac{6}{5}$.

Answer:

$\frac{6}{5}$ tons per acre (or 1.2 tons per acre)