\begin{tabular}{l} Question 2 \ Divide. Write your answer in lowest tehms. Leave your answer as an improper fraction or whole number, \ necessary. \ $$ \frac{3}{22} \div \frac{21}{2} $$ \ Question Help: $$ \square $$ Video $$ 1 \square $$ Video 2 \ \hline Message instructor D Post to forum \end{tabular}

Question

UpStudy AI · Accepted Answer

To solve the division of two fractions, follow these steps:

**Problem:**
$$
\frac{3}{22} \div \frac{21}{2}
$$

**Step 1: Rewrite the Division as Multiplication by the Reciprocal**

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of $$\frac{21}{2}$$ is $$\frac{2}{21}$$.

$$
\frac{3}{22} \div \frac{21}{2} = \frac{3}{22} \times \frac{2}{21}
$$

**Step 2: Multiply the Numerators and the Denominators**

Multiply the numerators (top numbers) together and the denominators (bottom numbers) together.

$$
\frac{3 \times 2}{22 \times 21} = \frac{6}{462}
$$

**Step 3: Simplify the Fraction**

To simplify $$\frac{6}{462}$$, find the greatest common divisor (GCD) of 6 and 462 and divide both the numerator and the denominator by that number.

1. **Find the GCD of 6 and 462:**
   - The factors of 6 are 1, 2, 3, 6.
   - The factors of 462 are numerous, but the largest common factor with 6 is 6.

2. **Divide both numerator and denominator by the GCD (6):**
   $$
   \frac{6 \div 6}{462 \div 6} = \frac{1}{77}
   $$

**Final Answer:**
$$
\frac{1}{77}
$$

This is the fraction in its lowest terms as an improper fraction.
$$ \frac{1}{77} $$

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Pre Algebra Questions