Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:57 minutes

Problem 32

Textbook Question

Multiply or divide as indicated. Write answers in lowest terms as needed. (21/8)*(4/7)

Verified step by step guidance

Identify the operation: We need to multiply two fractions, \( \frac{21}{8} \) and \( \frac{4}{7} \).

Multiply the numerators: Multiply 21 by 4 to get the numerator of the product.

Multiply the denominators: Multiply 8 by 7 to get the denominator of the product.

Simplify the fraction: Check if the resulting fraction can be simplified by finding the greatest common divisor (GCD) of the numerator and the denominator.

Write the simplified fraction: Divide both the numerator and the denominator by their GCD to express the fraction in its lowest terms.

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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, 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 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.

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 straightforward calculations.