Father's garden

John's father has a garden in the backyard. The dimensions of the garden are shown here.

A green rectangle is shown. The width is labeled as two and two-thirds feet. The length is labeled as seven and three-fourths feet.

Calculate the area of the garden.

You found the area of the garden. Explain briefly, without doing any calculations, how you would find 5/6 of this area.

Correct answer:

S =  20 ²⁄₃ = 62/3 ft²
S₂ =  17 ²⁄₉ = 155/9 ft²

Step-by-step explanation:

$$\begin{gathered} a=2\frac{2}{3}=2+\frac{2}{3}=\frac{2\cdot 3+2}{3}=\frac{6+2}{3}=\frac{8}{3}\doteq 2.6667\text{ft} \\ b=7\frac{3}{4}=7+\frac{3}{4}=\frac{7\cdot 4+3}{4}=\frac{28+3}{4}=\frac{31}{4}=7.75\text{ft} \\ S=a\cdot b=\frac{8}{3}\cdot \frac{31}{4}=\frac{8\cdot 31}{3\cdot 4}=\frac{248}{12}=\frac{62}{3}{\text{ft}}^2=20\frac{2}{3}{\text{ft}}^2=20.6667{\text{ft}}^2 \end{gathered}$$

$S_2=\frac{5}{6}\cdot S=\frac{5}{6}\cdot \frac{62}{3}=\frac{5\cdot 62}{6\cdot 3}=\frac{310}{18}=\frac{155}{9}{\text{ft}}^2=17.2222{\text{ft}}^2$

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