Use the properties of operations and rules for multiplying and dividing to solve 8/9 times -3/4 divided 1/9 times -4/5 divided 3/5

Answer 1

To solve the expression \( \frac{8}{9} \times \left(-\frac{3}{4}\right) \div \left(\frac{1}{9} \times \left(-\frac{4}{5}\right) \div \frac{3}{5}\right) \), we will break it down using the properties of operations step by step.

Step 1: Solve the parts inside the parentheses

First part: \[ \frac{1}{9} \times \left(-\frac{4}{5}\right) = -\frac{4}{45} \]

Second part: \[ -\frac{4}{45} \div \frac{3}{5} \] To divide by a fraction, we multiply by its reciprocal: \[ -\frac{4}{45} \times \frac{5}{3} = -\frac{4 \cdot 5}{45 \cdot 3} = -\frac{20}{135} \] Now, simplify \(-\frac{20}{135}\): \[ \text{GCD of } 20 \text{ and } 135 = 5 \] \[ -\frac{20 \div 5}{135 \div 5} = -\frac{4}{27} \]

Step 2: Substitute back and evaluate the entire expression

Now we substitute back into the main expression: \[ \frac{8}{9} \times \left(-\frac{3}{4}\right) \div \left(-\frac{4}{27}\right) \]

Multiply \( \frac{8}{9} \) and \( -\frac{3}{4} \): \[ \frac{8 \cdot -3}{9 \cdot 4} = -\frac{24}{36} \] Now simplify: \[ -\frac{24 \div 12}{36 \div 12} = -\frac{2}{3} \]

Now divide by \( -\frac{4}{27} \): To divide by a fraction, again we multiply by its reciprocal: \[ -\frac{2}{3} \div -\frac{4}{27} = -\frac{2}{3} \times -\frac{27}{4} = \frac{2 \cdot 27}{3 \cdot 4} = \frac{54}{12} \] Now simplify: \[ \frac{54 \div 6}{12 \div 6} = \frac{9}{2} \]

Thus, the final answer is: \[ \boxed{\frac{9}{2}} \]

Answer 2

whats it as an mixed number

Answer 3

To convert the improper fraction \(\frac{9}{2}\) into a mixed number, divide the numerator by the denominator.

1. Division: \(9 \div 2 = 4\) (which is the whole number part).
2. Remainder: \(9 - (2 \times 4) = 9 - 8 = 1\).

So, \(\frac{9}{2}\) can be expressed as:

\[ 4\frac{1}{2} \]

Thus, as a mixed number, \(\frac{9}{2}\) is:

\[ \boxed{4\frac{1}{2}} \]

Answer 4

wrong whats Use the properties of operations and rules for multiplying and dividing to solve 8/9 times -3/4 divided 1/9 times -4/5 divided 3/5

Answer 5

Let's correctly evaluate the expression

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

Step 1: Evaluate the inner expression \(\frac{1}{9} \times \left(-\frac{4}{5}\right) \div \frac{3}{5}\)

First, calculate \(\frac{1}{9} \times \left(-\frac{4}{5}\right)\):

\[ \frac{1}{9} \times \left(-\frac{4}{5}\right) = -\frac{4}{45} \]

Next, divide by \(\frac{3}{5}\):

\[ -\frac{4}{45} \div \frac{3}{5} = -\frac{4}{45} \times \frac{5}{3} = -\frac{4 \cdot 5}{45 \cdot 3} = -\frac{20}{135} \]

Now simplify \(-\frac{20}{135}\):

The greatest common divisor (GCD) of 20 and 135 is 5:

\[ -\frac{20 \div 5}{135 \div 5} = -\frac{4}{27} \]

Step 2: Evaluate the entire expression

Now substitute this value back into the original expression:

\[ \frac{8}{9} \times \left(-\frac{3}{4}\right) \div \left(-\frac{4}{27}\right) \]

Calculate \(\frac{8}{9} \times \left(-\frac{3}{4}\right)\):

\[ \frac{8 \times -3}{9 \times 4} = -\frac{24}{36} \]

Now simplify \(-\frac{24}{36}\):

The GCD of 24 and 36 is 12:

\[ -\frac{24 \div 12}{36 \div 12} = -\frac{2}{3} \]

Now divide by \(-\frac{4}{27}\):

To divide by a fraction, multiply by its reciprocal:

\[ -\frac{2}{3} \div -\frac{4}{27} = -\frac{2}{3} \times -\frac{27}{4} = \frac{2 \times 27}{3 \times 4} = \frac{54}{12} \]

Now simplify \(\frac{54}{12}\):

The GCD of 54 and 12 is 6:

\[ \frac{54 \div 6}{12 \div 6} = \frac{9}{2} \]

Final Answer

Thus, the resulting value of the expression is:

\[ \boxed{\frac{9}{2}} \]

To express \(\frac{9}{2}\) as a mixed number:

• \(9 \div 2 = 4\) remainder \(1\).

So, it can be expressed as:

\[ 4\frac{1}{2} \]

Thus, as a mixed number, the answer is:

\[ \boxed{4\frac{1}{2}} \]