8/9 ÷ (-72)/45
Understand the Problem
The question is presenting a division problem involving fractions. It requires simplifying or calculating the result of the expression provided.
Answer
The answer is $$ -\frac{5}{9} $$.
Answer for screen readers
The final answer is $$ -\frac{5}{9} $$.
Steps to Solve
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Rewrite the Division as Multiplication To divide fractions, we can multiply by the reciprocal of the second fraction. The expression is: $$ \frac{8}{9} \div \left(-\frac{72}{45}\right) $$ This becomes: $$ \frac{8}{9} \times \left(-\frac{45}{72}\right) $$
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Multiply the Numerators and the Denominators Now we multiply the numerators together and the denominators together: $$ \frac{8 \times -45}{9 \times 72} $$
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Calculate the Multiplication Compute the products:
- Numerator: $8 \times -45 = -360$
- Denominator: $9 \times 72 = 648$
So, we have: $$ \frac{-360}{648} $$
- Simplify the Fraction To simplify, we find the greatest common divisor (GCD) of 360 and 648. The GCD is 72. Now, divide both the numerator and the denominator by 72: $$ \frac{-360 \div 72}{648 \div 72} = \frac{-5}{9} $$
The final answer is $$ -\frac{5}{9} $$.
More Information
In fraction operations, dividing by a fraction is equivalent to multiplying by its reciprocal. Simplifying fractions helps to express answers in their simplest form.
Tips
- Forgetting to change the division into multiplication by the reciprocal.
- Not simplifying the fraction at the end.
- Miscalculating the products in the numerator and denominator.
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