Question
Solve:
(8/9) x (-3/4) divided by (1/9) x (-4/5) divided by (3/5)
(8/9) x (-3/4) divided by (1/9) x (-4/5) divided by (3/5)
Answers
GPT-4o mini
To solve the expression \((8/9) \times (-3/4) \div (1/9) \times (-4/5) \div (3/5)\), we'll break it down step by step.
1. **Calculate the first part:**
\[
(8/9) \times (-3/4) = \frac{8 \times -3}{9 \times 4} = \frac{-24}{36}
\]
Simplifying \(-24/36\):
\[
\frac{-24}{36} = \frac{-2}{3}
\]
2. **Calculate the second part:**
\[
(1/9) \times (-4/5) = \frac{1 \times -4}{9 \times 5} = \frac{-4}{45}
\]
3. **Put it together and perform the first division:**
Now we have:
\[
\frac{-2/3}{-4/45}
\]
When dividing two fractions, we multiply by the reciprocal:
\[
\frac{-2}{3} \div \frac{-4}{45} = \frac{-2}{3} \times \frac{45}{-4} = \frac{-2 \times 45}{3 \times -4} = \frac{90}{12}
\]
Simplifying \(90/12\):
\[
\frac{90}{12} = \frac{15}{2}
\]
4. **Now proceed with the final division:**
Next, we divide this result by \((3/5)\):
\[
\frac{15/2}{3/5} = \frac{15}{2} \div \frac{3}{5} = \frac{15}{2} \times \frac{5}{3} = \frac{15 \times 5}{2 \times 3} = \frac{75}{6}
\]
Simplifying \(75/6\):
\[
\frac{75}{6} = \frac{25}{2}
\]
So the final answer is:
\[
\boxed{\frac{25}{2}}
\]
1. **Calculate the first part:**
\[
(8/9) \times (-3/4) = \frac{8 \times -3}{9 \times 4} = \frac{-24}{36}
\]
Simplifying \(-24/36\):
\[
\frac{-24}{36} = \frac{-2}{3}
\]
2. **Calculate the second part:**
\[
(1/9) \times (-4/5) = \frac{1 \times -4}{9 \times 5} = \frac{-4}{45}
\]
3. **Put it together and perform the first division:**
Now we have:
\[
\frac{-2/3}{-4/45}
\]
When dividing two fractions, we multiply by the reciprocal:
\[
\frac{-2}{3} \div \frac{-4}{45} = \frac{-2}{3} \times \frac{45}{-4} = \frac{-2 \times 45}{3 \times -4} = \frac{90}{12}
\]
Simplifying \(90/12\):
\[
\frac{90}{12} = \frac{15}{2}
\]
4. **Now proceed with the final division:**
Next, we divide this result by \((3/5)\):
\[
\frac{15/2}{3/5} = \frac{15}{2} \div \frac{3}{5} = \frac{15}{2} \times \frac{5}{3} = \frac{15 \times 5}{2 \times 3} = \frac{75}{6}
\]
Simplifying \(75/6\):
\[
\frac{75}{6} = \frac{25}{2}
\]
So the final answer is:
\[
\boxed{\frac{25}{2}}
\]
Sage
Wrong
GPT-4o mini
Let’s carefully re-evaluate the expression step by step. The expression we need to solve is:
\[
\left(\frac{8}{9} \times \left(-\frac{3}{4}\right)\right) \div \left(\frac{1}{9} \times \left(-\frac{4}{5}\right)\right) \div \left(\frac{3}{5}\right)
\]
1. **Calculate the first multiplication:**
\[
\frac{8}{9} \times \left(-\frac{3}{4}\right) = \frac{8 \times -3}{9 \times 4} = \frac{-24}{36} = -\frac{2}{3} \quad (\text{after simplifying} -\frac{24}{36})
\]
2. **Calculate the second multiplication:**
\[
\frac{1}{9} \times \left(-\frac{4}{5}\right) = \frac{1 \times -4}{9 \times 5} = \frac{-4}{45}
\]
3. **Now let's rewrite the expression using these results:**
\[
\left(-\frac{2}{3}\right) \div \left(-\frac{4}{45}\right)
\]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
-\frac{2}{3} \times \left(-\frac{45}{4}\right) = \frac{2 \times 45}{3 \times 4} = \frac{90}{12} = \frac{15}{2} \quad (\text{after simplifying})
\]
4. **Now we take this result and divide by \(\frac{3}{5}\):**
\[
\frac{15}{2} \div \frac{3}{5}
\]
Again, we multiply by the reciprocal:
\[
\frac{15}{2} \times \frac{5}{3} = \frac{15 \times 5}{2 \times 3} = \frac{75}{6}
\]
Simplifying \(\frac{75}{6}\):
\[
\frac{75}{6} = \frac{25}{2} \quad (\text{after dividing numerator and denominator by 3})
\]
Thus, the final answer is:
\[
\boxed{\frac{25}{2}}
\]
It seems the solution derived has been consistent. If there's an error or a different context in which the expression needs to be evaluated, please specify it so that I can assist accurately!
\[
\left(\frac{8}{9} \times \left(-\frac{3}{4}\right)\right) \div \left(\frac{1}{9} \times \left(-\frac{4}{5}\right)\right) \div \left(\frac{3}{5}\right)
\]
1. **Calculate the first multiplication:**
\[
\frac{8}{9} \times \left(-\frac{3}{4}\right) = \frac{8 \times -3}{9 \times 4} = \frac{-24}{36} = -\frac{2}{3} \quad (\text{after simplifying} -\frac{24}{36})
\]
2. **Calculate the second multiplication:**
\[
\frac{1}{9} \times \left(-\frac{4}{5}\right) = \frac{1 \times -4}{9 \times 5} = \frac{-4}{45}
\]
3. **Now let's rewrite the expression using these results:**
\[
\left(-\frac{2}{3}\right) \div \left(-\frac{4}{45}\right)
\]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
-\frac{2}{3} \times \left(-\frac{45}{4}\right) = \frac{2 \times 45}{3 \times 4} = \frac{90}{12} = \frac{15}{2} \quad (\text{after simplifying})
\]
4. **Now we take this result and divide by \(\frac{3}{5}\):**
\[
\frac{15}{2} \div \frac{3}{5}
\]
Again, we multiply by the reciprocal:
\[
\frac{15}{2} \times \frac{5}{3} = \frac{15 \times 5}{2 \times 3} = \frac{75}{6}
\]
Simplifying \(\frac{75}{6}\):
\[
\frac{75}{6} = \frac{25}{2} \quad (\text{after dividing numerator and denominator by 3})
\]
Thus, the final answer is:
\[
\boxed{\frac{25}{2}}
\]
It seems the solution derived has been consistent. If there's an error or a different context in which the expression needs to be evaluated, please specify it so that I can assist accurately!