Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 25

Chapter 1, Problem 25

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

Verified step by step guidance

Identify the operation: You are asked to multiply two fractions, \( \frac{4}{5} \) and \( \frac{6}{7} \).

Multiply the numerators together: \( 4 \times 6 = 24 \).

Multiply the denominators together: \( 5 \times 7 = 35 \).

Write the product as a single fraction: \( \frac{24}{35} \).

Check if the fraction \( \frac{24}{35} \) can be simplified by finding the greatest common divisor (GCD) of 24 and 35, and then divide numerator and denominator by the GCD if possible.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Multiplication of Fractions

To multiply fractions, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. For example, (a/b) * (c/d) = (a*c) / (b*d).

Simplifying Fractions

After performing multiplication or division, simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD) to write the fraction in lowest terms.

Writing Answers in Lowest Terms

A fraction is in lowest terms when the numerator and denominator share no common factors other than 1. Simplifying ensures the answer is expressed in its simplest and most understandable form.

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