Multiply or divide as indicated. Write answers in lowest terms as needed. 2(5/8)/1(15/32)

Verified step by step guidance

1. First, simplify the expression \( \frac{2 \times \frac{5}{8}}{1 \times \frac{15}{32}} \) by multiplying the numerators and denominators separately.
2. Multiply the numerators: \( 2 \times 5 = 10 \).
3. Multiply the denominators: \( 1 \times 15 = 15 \).
4. Now, rewrite the expression as \( \frac{10}{8} \div \frac{15}{32} \).
5. To divide fractions, multiply by the reciprocal: \( \frac{10}{8} \times \frac{32}{15} \).

Key Concepts

Multiplication of Fractions

To multiply fractions, you multiply the numerators together and the denominators together. For example, multiplying 2/3 by 4/5 results in (2*4)/(3*5) = 8/15. This concept is essential for solving problems that involve multiplying fractions, as it simplifies the process and helps in finding the product efficiently.

Division of Fractions

Dividing fractions involves multiplying by the reciprocal of the divisor. For instance, to divide 2/3 by 4/5, you would multiply 2/3 by 5/4, resulting in (2*5)/(3*4) = 10/12. Understanding this concept is crucial for accurately performing division operations with fractions.

Simplifying Fractions

Simplifying fractions means reducing them to their lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD). For example, the fraction 10/12 can be simplified to 5/6. This concept is important for ensuring that answers are presented in the simplest form, making them easier to understand and use.