Multiply or divide as indicated. Write answers in lowest terms as needed. $6\frac{3}{4}÷\frac{3}{8}$

Verified step by step guidance

1. Identify the expression to simplify: \(6 \times \frac{3}{4} \div \frac{3}{8}\).
2. Rewrite the division as multiplication by the reciprocal: \(6 \times \frac{3}{4} \times \frac{8}{3}\).
3. Multiply the numerators together and the denominators together: \(\frac{6 \times 3 \times 8}{1 \times 4 \times 3}\).
4. Simplify the fraction by canceling common factors in numerator and denominator.
5. Write the simplified fraction or whole number as the final answer in lowest terms.

Key Concepts

Multiplication and Division of Fractions

To multiply fractions, multiply the numerators together and the denominators together. For division, multiply by the reciprocal of the divisor fraction. This means flipping the numerator and denominator of the fraction you are dividing by before multiplying.

Simplifying Fractions

After performing multiplication or division, simplify the resulting fraction by dividing the numerator and denominator by their greatest common divisor (GCD). This reduces the fraction to its lowest terms, making it easier to interpret and use.

Converting Whole Numbers to Fractions

Whole numbers can be expressed as fractions by placing them over 1 (e.g., 6 = 6/1). This allows consistent application of fraction operations like multiplication and division when whole numbers are involved.