On the floor 2

The living room's floor area is 9 7/9 m². A carpet covering an area of 5 5/8 m² is placed on the floor. Find the area of the room that is not covered with carpet.

Final Answer:

x =  4 ¹¹⁄₇₂ = 299/72 m²

Step-by-step explanation:

$$\begin{gathered} a=9\frac{7}{9}=9+\frac{7}{9}=\frac{9\cdot 9+7}{9}=\frac{81+7}{9}=\frac{88}{9}\doteq 9.7778{\text{m}}^2 \\ c=5\frac{5}{8}=5+\frac{5}{8}=\frac{5\cdot 8+5}{8}=\frac{40+5}{8}=\frac{45}{8}=5.625{\text{m}}^2 \\ x=a-c=\frac{88}{9}-\frac{45}{8}=\frac{704}{72}-\frac{405}{72}=\frac{704-405}{72}=\frac{299}{72}=\frac{299}{72}{\text{m}}^2=4\frac{11}{72}{\text{m}}^2=4.1528{\text{m}}^2 \end{gathered}$$

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