1. How many times is the value of the expression

$$
2 \cdot \frac{7 \frac{2}{3}:\left(2 \frac{2}{3}+0.5: 1 \frac{1}{2}\right)}{\left(2 \frac{1}{3}-1 \frac{1}{9} \cdot 0.75\right): 7 \frac{1}{3}}
$$

smaller than the number 2024?
1. How many times is the value of the expression

$$
2 \cdot \frac{7 \frac{2}{3}:\left(2 \frac{2}{3}+0.5: 1 \frac{1}{2}\right)}{\left(2 \frac{1}{3}-1 \frac{1}{9} \cdot 0.75\right): 7 \frac{1}{3}}
$$

smaller than the number 2024?

## Solution.

The value of the given expression is:

$$
\begin{gathered}
2 \cdot \frac{7 \frac{2}{3}:\left(2 \frac{2}{3}+0.5: 1 \frac{1}{2}\right)}{\left(2 \frac{1}{3}-1 \frac{1}{9} \cdot 0.75\right): 7 \frac{1}{3}}= \\
2 \cdot \frac{\frac{23}{3}:\left(\frac{8}{3}+\frac{1}{2}: \frac{3}{2}\right)}{\left(\frac{7}{3}-\frac{10}{9} \cdot \frac{3}{4}\right): \frac{22}{3}}= \\
2 \cdot \frac{\frac{23}{3}:\left(\frac{8}{3}+\frac{1}{3}\right)}{\left(\frac{7}{3}-\frac{5}{6}\right): \frac{22}{3}}= \\
2 \cdot \frac{\frac{23}{3}: 3}{\frac{9}{6}: \frac{22}{3}}= \\
2 \cdot \frac{23}{9}: \frac{9}{44}= \\
=\frac{2024}{81}
\end{gathered}
$$

Note: If the student solved it in a different way, the solution should be graded according to the principle:

1 POINT for correctly writing all decimal and mixed numbers in the form of fractions, 1 POINT for calculating the value of the parenthesis in the numerator, 1 POINT for calculating the value of the parenthesis in the denominator, 1 POINT for further simplifying the numerator and denominator, 1 POINT for calculating the value of the given expression, and 1 POINT for the result.