Question

Use the properties of operations and rules for multiplying and dividing to solve:

(9)÷(5/4)×(7/9)×(−5)÷(7/2)

(1 point)
Responses

−1,225/8
negative Start Fraction 1,225 over 8 End Fraction

8
8

1,225/8
Start Fraction 1,225 over 8 End Fraction

−8

Answer 1

To solve the expression \((9) ÷ (5/4) × (7/9) × (−5) ÷ (7/2)\), let's follow the order of operations while utilizing multiplication and division rules.

### Step 1: Rewrite the division as multiplication by the reciprocal.

1. Rewrite \(9 ÷ (5/4)\) as \(9 × (4/5)\):
\[
9 × (4/5) = \frac{9 × 4}{5} = \frac{36}{5}
\]

2. Rewrite \(÷ (7/2)\) as \(× (2/7)\):
\[
\frac{36}{5} × \frac{2}{7}
\]

Combining the above, we have:
\[
\frac{36}{5} × \frac{2}{7} = \frac{36 × 2}{5 × 7} = \frac{72}{35}
\]

### Step 2: Now, incorporate the other factors \((7/9)\) and \((-5)\):

Continuing from the last expression:
\[
(−5) × (\frac{72}{35}) = \frac{−5 × 72}{35} = \frac{−360}{35}
\]

### Step 3: Now, multiply by \(7/9\):
\[
\frac{−360}{35} × \frac{7}{9} = \frac{−360 × 7}{35 × 9}
\]

### Step 4: Simplify that:

Calculating the numerator:
\[
−360 × 7 = -2520
\]

Calculating the denominator:
\[
35 × 9 = 315
\]

### Step 5: Combine the results:
Final expression:
\[
\frac{-2520}{315}
\]

### Step 6: Simplify the fraction:
To simplify \(-2520/315\), we find the GCD:
\[
2520 ÷ 315 = 8
\]
This can also be confirmed by reducing it:
\[
\frac{-2520 ÷ 315}{315 ÷ 315} = \frac{-8}{1}
\]

Thus, we obtain:
\[
-8
\]

The final answer is:
\[
\text{Negative } 8
\]
So the correct response is:
\[
−8
\]