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

(9)÷(5/4)×(7/9)×(−5)÷(7/2)

(1 point)
Responses

8
8

−8
negative 8

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

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

To simplify the expression \( (9) \div (5/4) \times (7/9) \times (-5) \div (7/2) \), we can follow the properties of operations step by step.

  1. Rewrite the expression:

    \[ 9 \div \frac{5}{4} \times \frac{7}{9} \times (-5) \div \frac{7}{2} \]

  2. Convert divisions into multiplications:

    Dividing by a fraction is the same as multiplying by its reciprocal.

    \[ 9 \times \frac{4}{5} \times \frac{7}{9} \times (-5) \times \frac{2}{7} \]

  3. Simplify the expression:

    Now we can cancel out terms where possible.

    • The \( 9 \) in \( 9 \times \frac{7}{9} \) cancels out with the \( 9 \) in the denominator:

    \[ 1 \times \frac{4}{5} \times 7 \times (-5) \times \frac{2}{7} \]

    • The \( 7 \) in \( \frac{4}{5} \times \frac{7}{9} \) cancels out with the \( 7 \) in the denominator:

    \[ 1 \times \frac{4}{5} \times (-5) \times 2 \]

  4. Calculate:

    Now we can multiply the remaining terms:

    \[ \frac{4}{5} \times (-5) \times 2 = \frac{4 \times -5 \times 2}{5} \]

    • Calculating:

    \[ = \frac{-40}{5} = -8 \]

So the final answer is:

\[ \boxed{-8} \]