Question

Solve

8/9 times -3/4 times 9/1 times -4/5 times 5/3

Answer 1

To solve the expression \( \frac{8}{9} \times \left(-\frac{3}{4}\right) \times \frac{9}{1} \times \left(-\frac{4}{5}\right) \times \frac{5}{3} \), we can multiply the fractions step-by-step.

First, let's rearrange the expression for clarity:

\[
\left(\frac{8}{9} \times \left(-\frac{3}{4}\right) \times \frac{9}{1} \times \left(-\frac{4}{5}\right) \times \frac{5}{3}\right)
\]

Next, let's group the fractions together and put the negative signs in a way that's easier to handle:

\[
= \frac{8 \times (-3) \times 9 \times (-4) \times 5}{9 \times 4 \times 1 \times 5 \times 3}
\]

Now, let's calculate the numerator:

\[
8 \times (-3) = -24
\]
\[
-24 \times 9 = -216
\]
\[
-216 \times (-4) = 864
\]
\[
864 \times 5 = 4320
\]

So the numerator is \( 4320 \).

Next, let's calculate the denominator:

\[
9 \times 4 = 36
\]
\[
36 \times 1 = 36
\]
\[
36 \times 5 = 180
\]
\[
180 \times 3 = 540
\]

So the denominator is \( 540 \).

Now we have:

\[
= \frac{4320}{540}
\]

Next, we simplify \( \frac{4320}{540} \). To do this, we can divide both the numerator and denominator by their greatest common divisor (GCD).

Calculating the GCD:

- The prime factorization of 4320 is \( 2^4 \times 3^3 \times 5 \).
- The prime factorization of 540 is \( 2 \times 3^3 \times 5 \).

The GCD is \( 2^1 \times 3^3 \times 5 = 90 \).

Now we divide both the numerator and denominator by \( 90 \):

\[
\frac{4320 \div 90}{540 \div 90} = \frac{48}{6} = 8
\]

Thus, the final result is:

\[
\boxed{8}
\]