Question
\( -\frac{9}{10} \div\left(-\frac{3}{2}\right)=\square \) (Simplify your answer. Type an integer or a fraction.)
Ask by Simpson Edwards. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(\frac{3}{5}\)
Solution
**Step 1: Rewrite the Division as Multiplication by the Reciprocal**
\[
-\frac{9}{10} \div \left(-\frac{3}{2}\right) = -\frac{9}{10} \times \left(-\frac{2}{3}\right)
\]
**Step 2: Multiply the Two Fractions**
Two negatives multiplied together give a positive result, so we have:
\[
-\frac{9}{10} \times \left(-\frac{2}{3}\right) = \frac{9}{10} \times \frac{2}{3}
\]
**Step 3: Multiply Numerators and Denominators**
\[
\frac{9 \times 2}{10 \times 3} = \frac{18}{30}
\]
**Step 4: Simplify the Fraction**
Divide the numerator and denominator by their greatest common divisor, which is 6:
\[
\frac{18 \div 6}{30 \div 6} = \frac{3}{5}
\]
\(\boxed{\frac{3}{5}}\)
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Simplify this solution Bonus Knowledge
To solve \( -\frac{9}{10} \div\left(-\frac{3}{2}\right) \), first, we can change the division of fractions into multiplication by the reciprocal. So, we rewrite it as: \[ -\frac{9}{10} \times -\frac{2}{3} \] Multiplying the fractions gives us: \[ \frac{9 \times 2}{10 \times 3} = \frac{18}{30} \] Now, we can simplify \(\frac{18}{30}\) by dividing both the numerator and denominator by their greatest common divisor, which is 6: \[ \frac{18 \div 6}{30 \div 6} = \frac{3}{5} \] Thus, the answer is: \[ \frac{3}{5} \]
