Find the following quotient. Reduce to lowest terms. $$ \frac{15}{34} \div 5 $$

Question

UpStudy AI · Accepted Answer

To find the quotient of $$\frac{15}{34}$$ divided by $$5$$ and reduce it to its lowest terms, follow these steps:

1. **Express the Division as Multiplication:**

Dividing by a number is the same as multiplying by its reciprocal. So,
   $$
   \frac{15}{34} \div 5 = \frac{15}{34} \times \frac{1}{5}
   $$

2. **Multiply the Fractions:**

Multiply the numerators together and the denominators together:
   $$
   \frac{15 \times 1}{34 \times 5} = \frac{15}{170}
   $$

3. **Simplify the Fraction:**

To reduce $$\frac{15}{170}$$ to its lowest terms, find the greatest common divisor (GCD) of 15 and 170.

- **Factors of 15:** 1, 3, 5, 15
   - **Factors of 170:** 1, 2, 5, 10, 17, 34, 85, 170

The greatest common divisor is **5**.

4. **Divide Both Numerator and Denominator by the GCD:**
   $$
   \frac{15 \div 5}{170 \div 5} = \frac{3}{34}
   $$

So, the quotient reduced to its lowest terms is:

$$
\boxed{\dfrac{3}{34}}
$$
The quotient is $$\frac{3}{34}$$.

Find the following quotient. Reduce to lowest terms. \[ \frac{15}{34} \div 5 \]