Multiply or divide as indicated. Write answers in lowest terms as needed. $\frac{7}{5}÷\frac{3}{10}$

Verified step by step guidance

1. Identify the problem as a division of two fractions: \(\frac{7}{5} \div \frac{3}{10}\).
2. Recall that dividing by a fraction is the same as multiplying by its reciprocal. So rewrite the expression as \(\frac{7}{5} \times \frac{10}{3}\).
3. Multiply the numerators together and the denominators together: numerator = \(7 \times 10\), denominator = \(5 \times 3\).
4. Write the product as a single fraction: \(\frac{7 \times 10}{5 \times 3}\).
5. Simplify the fraction by finding the greatest common divisor (GCD) of numerator and denominator and dividing both by it to get the fraction in lowest terms.

Key Concepts

Dividing Fractions

Dividing fractions involves multiplying the first fraction by the reciprocal of the second. The reciprocal of a fraction is obtained by swapping its numerator and denominator. For example, dividing by 3/10 is the same as multiplying by 10/3.

Multiplying Fractions

To multiply fractions, multiply the numerators together and the denominators together. For instance, (7/5) × (10/3) equals (7×10)/(5×3). This process combines the fractions into a single fraction.

Simplifying Fractions

Simplifying fractions means reducing them to their lowest terms by dividing numerator and denominator by their greatest common divisor (GCD). This makes the fraction easier to understand and use in further calculations.