Multiply or divide as indicated. Write answers in lowest terms as needed. (4/5)*(6/7)

Verified step by step guidance

1. Identify the operation: This problem requires multiplication of two fractions.
2. Multiply the numerators: Multiply the numerator of the first fraction (4) by the numerator of the second fraction (6).
3. Multiply the denominators: Multiply the denominator of the first fraction (5) by the denominator of the second fraction (7).
4. Write the result as a new fraction: Place the product of the numerators over the product of the denominators.
5. Simplify the fraction: If possible, reduce the fraction to its lowest terms by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by it.

Key Concepts

Multiplication of Fractions

To multiply fractions, you multiply the numerators together and the denominators together. For example, in the expression (a/b) * (c/d), the result is (a*c)/(b*d). This process simplifies the multiplication of fractions into a straightforward operation, allowing for easy calculation of the product.

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.

Dividing Fractions

Dividing fractions involves multiplying by the reciprocal of the divisor. For instance, to divide (a/b) by (c/d), you multiply (a/b) by (d/c). This method transforms the division into a multiplication problem, simplifying the process and allowing for easier calculations.