Multiply or divide as indicated. Write answers in lowest terms as needed. 2(1/2)/1(5/7)

Verified step by step guidance

1. First, rewrite the expression \( 2\left(\frac{1}{2}\right) \div 1\left(\frac{5}{7}\right) \) as a multiplication problem by using the reciprocal of the second fraction.
2. The reciprocal of \( 1\left(\frac{5}{7}\right) \) is \( \frac{7}{5} \).
3. Rewrite the division as multiplication: \( 2\left(\frac{1}{2}\right) \times \frac{7}{5} \).
4. Simplify \( 2\left(\frac{1}{2}\right) \) to \( 1 \) because \( 2 \times \frac{1}{2} = 1 \).
5. Now multiply the simplified expression: \( 1 \times \frac{7}{5} \).

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. This means flipping the second fraction and then proceeding with multiplication. Understanding these operations is crucial for simplifying complex fraction expressions.

Lowest Terms

A fraction is in lowest terms when the numerator and denominator have no common factors other than 1. To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD). This concept is essential for presenting answers in their simplest form, which is often required in mathematical problems.

Mixed Numbers and Improper Fractions

Mixed numbers consist of a whole number and a fraction, while improper fractions have numerators larger than their denominators. Converting between these forms is often necessary for operations involving fractions. Understanding how to manipulate these forms helps in accurately performing calculations and simplifying results.