Question

try one without the area model!
compare \\(\frac{9}{5}\\) and \\(\frac{10}{8}\\) by using multiplication. first, make like units.
\\(\frac{9}{5} = \frac{9 \times square}{5 \times square} = \frac{square}{square}\\) \\(\frac{10}{8} = \frac{10 \times square}{8 \times square} = \frac{square}{square}\\)

Explanation:

Step1: Find common denominator for 5 and 8

The least common denominator of 5 and 8 is $5\times8 = 40$. So for $\frac{9}{5}$, we multiply numerator and denominator by 8.
$\frac{9}{5}=\frac{9\times8}{5\times8}=\frac{72}{40}$

Step2: Multiply numerator and denominator of $\frac{10}{8}$ by 5

For $\frac{10}{8}$, we multiply numerator and denominator by 5 to get the same denominator 40.
$\frac{10}{8}=\frac{10\times5}{8\times5}=\frac{50}{40}$

Answer:

For $\frac{9}{5}=\frac{9\times\boldsymbol{8}}{5\times\boldsymbol{8}}=\frac{\boldsymbol{72}}{\boldsymbol{40}}$; for $\frac{10}{8}=\frac{10\times\boldsymbol{5}}{8\times\boldsymbol{5}}=\frac{\boldsymbol{50}}{\boldsymbol{40}}$