Find the following quotient. Reduce to lowest terms. $$ \frac{20}{14} \div \frac{15}{23} $$

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UpStudy AI · Accepted Answer

To find the quotient $$\frac{20}{14} \div \frac{15}{23}$$ and reduce it to its lowest terms, follow these steps:

1. **Convert Division to Multiplication:**
   $$
   \frac{20}{14} \div \frac{15}{23} = \frac{20}{14} \times \frac{23}{15}
   $$

2. **Factor and Simplify Before Multiplying:**
   - **Factor the Numbers:**
     $$
     20 = 4 \times 5,\quad 14 = 2 \times 7,\quad 15 = 3 \times 5,\quad 23 \text{ is prime}
     $$
   - **Set Up the Multiplication:**
     $$
     \frac{4 \times 5}{2 \times 7} \times \frac{23}{3 \times 5}
     $$
   - **Cancel Common Factors:**
     - The $$5$$ in the numerator and denominator cancels out:
       $$
       \frac{4}{2 \times 7} \times \frac{23}{3}
       $$
     - Simplify $$\frac{4}{2}$$ to $$2$$:
       $$
       \frac{2}{7} \times \frac{23}{3}
       $$

3. **Multiply the Simplified Fractions:**
   $$
   \frac{2 \times 23}{7 \times 3} = \frac{46}{21}
   $$

4. **Verify Lowest Terms:**
   - The greatest common divisor (GCD) of 46 and 21 is 1, so $$\frac{46}{21}$$ is already in its lowest terms.

**Final Answer:**
$$
\boxed{\dfrac{46}{21}}
$$
The quotient is $$\frac{46}{21}$$.

Find the following quotient. Reduce to lowest terms.

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