Question

are \\(\frac{7\frac{3}{5}}{1.2}\\) and \\(\frac{22\frac{4}{5}}{3\frac{3}{5}}\\) in a proportional relationship?
drag and drop the choices to the boxes to correctly complete the statements.
\\(\frac{7\frac{3}{5}}{1.2}\\) and \\(\frac{22\frac{4}{5}}{3\frac{3}{5}}\\) \\(\square\\) in a proportional relationship because they \\(\square\\) equivalent.
\\(\frac{7\frac{3}{5}}{1.2}\\) simplifies to \\(\square\\) and \\(\frac{22\frac{4}{5}}{3\frac{3}{5}}\\) simplifies to \\(\square\\).
\\(\boxed{are}\\) \\(\boxed{are not}\\) \\(\boxed{\frac{9}{4}}\\) \\(\boxed{\frac{13}{2}}\\) \\(\boxed{6}\\) \\(\boxed{\frac{19}{3}}\\) \\(\boxed{\frac{38}{7}}\\)

Explanation:

Step1: Convert mixed numbers to fractions

First fraction numerator: $7\frac{3}{5} = \frac{7\times5 + 3}{5} = \frac{38}{5}$
First fraction denominator: $1.2 = \frac{6}{5}$
Second fraction numerator: $22\frac{4}{5} = \frac{22\times5 + 4}{5} = \frac{114}{5}$
Second fraction denominator: $3\frac{3}{5} = \frac{3\times5 + 3}{5} = \frac{18}{5}$

Step2: Simplify first complex fraction

Dividing by a fraction = multiply by reciprocal:
$\frac{\frac{38}{5}}{\frac{6}{5}} = \frac{38}{5} \times \frac{5}{6} = \frac{38}{6} = \frac{19}{3}$

Step3: Simplify second complex fraction

Dividing by a fraction = multiply by reciprocal:
$\frac{\frac{114}{5}}{\frac{18}{5}} = \frac{114}{5} \times \frac{5}{18} = \frac{114}{18} = \frac{19}{3}$

Step4: Compare simplified values

Both fractions simplify to $\frac{19}{3}$, so they are equivalent, meaning they have a proportional relationship.

Answer:

$\frac{7\frac{3}{5}}{1.2}$ and $\frac{22\frac{4}{5}}{3\frac{3}{5}}$ $\boldsymbol{are}$ in a proportional relationship because they $\boldsymbol{are}$ equivalent.
$\frac{7\frac{3}{5}}{1.2}$ simplifies to $\boldsymbol{\frac{19}{3}}$ and $\frac{22\frac{4}{5}}{3\frac{3}{5}}$ simplifies to $\boldsymbol{\frac{19}{3}}$.