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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1:35 minutes

Problem 43

Textbook Question

Multiply or divide as indicated. Write answers in lowest terms as needed. (3/4)/12

Verified step by step guidance

Convert the division of a fraction by a whole number into a multiplication problem by taking the reciprocal of the whole number.

The reciprocal of 12 is \( \frac{1}{12} \).

Rewrite the expression \( \frac{3}{4} \div 12 \) as \( \frac{3}{4} \times \frac{1}{12} \).

Multiply the numerators: \( 3 \times 1 \).

Multiply the denominators: \( 4 \times 12 \).

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Key Concepts

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

Fraction Division

Dividing fractions involves multiplying by the reciprocal of the divisor. In this case, to divide (3/4) by 12, you can rewrite 12 as a fraction (12/1) and then multiply (3/4) by the reciprocal of (12/1), which is (1/12). This process simplifies the operation and allows for easier calculation.

Lowest Terms

Writing a fraction in lowest terms means simplifying it so that the numerator and denominator have no common factors other than 1. This is achieved by dividing both the numerator and denominator by their greatest common divisor (GCD). For example, if the result of a division yields a fraction like 3/48, it can be simplified to 1/16.

Multiplying Fractions

When multiplying fractions, you multiply the numerators together and the denominators together. For instance, if you multiply (3/4) by (1/12), you calculate (3 * 1) for the numerator and (4 * 12) for the denominator, resulting in a new fraction. This method is essential for both multiplication and division of fractions.