Answer:
Four
Step-by-step explanation:
We have the expression [tex](-5)(\frac{-2}{7})(\frac{4}{11})(-9)[/tex].
Now, four different students have applied different properties to rewrite the expression above.
1. Mitul used commutative property i.e. ab = ba
So, [tex][(-5)(\frac{-2}{7})][(\frac{4}{11})(-9)][/tex] = [tex][(\frac{-2}{7})(-5)][(-9)(\frac{4}{11})][/tex].
2. Stacy used associative property i.e. a(bc) = (ab)c
Then, [tex]-5[\frac{-2}{7}(\frac{4}{11}\times -9)][/tex] = [tex]-5[(\frac{-2}{7}\times \frac{4}{11})(-9)][/tex]
3. Tom used associative property followed by commutative property
Thus, [tex]-5[\frac{-2}{7}(\frac{4}{11}\times -9)][/tex] = [tex]-5[(\frac{-2}{7}\times \frac{4}{11})(-9)][/tex] = [tex]-5[(\frac{4}{11}\times \frac{-2}{7})(-9)][/tex]
4. Walt used commutative property followed by associative property
So, [tex][(-5)(\frac{-2}{7})][(\frac{4}{11})(-9)][/tex] = [tex][(\frac{-2}{7})(-5)][(-9)(\frac{4}{11})][/tex] = [tex](\frac{-2}{7})[(-5\times -9)(\frac{4}{11})][/tex] = [tex](\frac{-2}{7})[(-5)(-9\times \frac{4}{11})][/tex].
Hence, we see that all the four students have rewritten the expressions equivalent to the original expression.
