Multiply or divide as indicated. Write answers in lowest terms as needed. (7/5)/(3/10)

Verified step by step guidance

1. Identify the operation: This problem involves division of two fractions, \( \frac{7}{5} \div \frac{3}{10} \).
2. Recall the rule for dividing fractions: To divide by a fraction, multiply by its reciprocal. The reciprocal of \( \frac{3}{10} \) is \( \frac{10}{3} \).
3. Rewrite the division as multiplication: \( \frac{7}{5} \times \frac{10}{3} \).
4. Multiply the numerators: \( 7 \times 10 \). Multiply the denominators: \( 5 \times 3 \).
5. Simplify the resulting fraction by finding the greatest common divisor (GCD) of the numerator and the denominator, and divide both by the GCD to write the fraction in lowest terms.

Key Concepts

Fraction Division

Dividing fractions involves multiplying by the reciprocal of the divisor. To divide two fractions, you take the first fraction and multiply it by the reciprocal of the second fraction. For example, dividing (a/b) by (c/d) is equivalent to (a/b) * (d/c). This method simplifies the process and allows for easier calculations.

Lowest Terms

A fraction is in lowest terms when the numerator and denominator have no common factors other than 1. To simplify a fraction, you can divide both the numerator and denominator by their greatest common divisor (GCD). This ensures that the fraction is expressed in its simplest form, making it easier to understand and work with.

Multiplication of Fractions

Multiplying fractions involves multiplying the numerators together and the denominators together. For instance, to multiply (a/b) by (c/d), you calculate (a*c)/(b*d). This straightforward approach allows for quick calculations and is essential for both multiplication and division of fractions, as division can be transformed into multiplication by using reciprocals.