Use the properties of operations and rules for multiplying and dividing to solve: (8/9) x (3/4) divided by (1/9) x (-4/5) divided by (3/5)

Let's solve the expression step by step using the properties of multiplication and division:

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

### Step 1: Simplify the first part \(\frac{8}{9} \times \frac{3}{4}\)
Multiply the numerators and the denominators:
\[
\frac{8}{9} \times \frac{3}{4} = \frac{8 \times 3}{9 \times 4} = \frac{24}{36} = \frac{2}{3}
\]

### Step 2: Simplify the second part \(\frac{1}{9} \times \frac{-4}{5} \div \frac{3}{5}\)
First, multiply \(\frac{1}{9} \times \frac{-4}{5}\):
\[
\frac{1}{9} \times \frac{-4}{5} = \frac{1 \times -4}{9 \times 5} = \frac{-4}{45}
\]

Now, divide \(\frac{-4}{45}\) by \(\frac{3}{5}\), which is equivalent to multiplying by the reciprocal of \(\frac{3}{5}\):
\[
\frac{-4}{45} \div \frac{3}{5} = \frac{-4}{45} \times \frac{5}{3} = \frac{-4 \times 5}{45 \times 3} = \frac{-20}{135} = \frac{-4}{27}
\]

### Step 3: Divide the two results from Steps 1 and 2
Now, divide \(\frac{2}{3}\) by \(\frac{-4}{27}\):
\[
\frac{2}{3} \div \frac{-4}{27} = \frac{2}{3} \times \frac{27}{-4} = \frac{2 \times 27}{3 \times -4} = \frac{54}{-12} = \frac{-9}{2}
\]

### Final Answer:
\[
\boxed{\frac{-9}{2}}
\]

Would you like a detailed explanation of any step or clarification?

Here are 5 related questions for practice:
1. Simplify \(\frac{5}{6} \times \frac{3}{8} \div \left( \frac{2}{7} \times \frac{-9}{4} \div \frac{1}{2} \right)\).
2. What is \(\frac{7}{8} \times \frac{-2}{5} \div \left( \frac{-3}{4} \times \frac{1}{9} \right)\)?
3. Solve \(\frac{12}{5} \times \frac{2}{3} \div \left( \frac{6}{7} \times \frac{1}{2} \div \frac{5}{8} \right)\).
4. Multiply and simplify: \(\frac{-9}{11} \times \frac{5}{6} \div \frac{3}{4}\).
5. Simplify \(\frac{4}{15} \times \frac{6}{8} \div \left( \frac{2}{5} \times \frac{-3}{7} \right)\).

**Tip**: When dividing fractions, remember to multiply by the reciprocal of the divisor.

Learn how to solve a complex fraction multiplication and division problem involving (8/9) × (3/4) ÷ (1/9) × (-4/5) ÷ (3/5). This step-by-step solution explains the properties of operations for fraction arithmetic, ideal for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation