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 4

Chapter 1, Problem 4

The reciprocal of 6/2 is 3/1.

Verified step by step guidance

Recall that the reciprocal of a fraction \(\frac{a}{b}\) is obtained by swapping the numerator and denominator, resulting in \(\frac{b}{a}\).

Start with the given fraction \(\frac{6}{2}\).

Find the reciprocal by swapping the numerator and denominator: the reciprocal of \(\frac{6}{2}\) is \(\frac{2}{6}\).

Simplify the reciprocal fraction \(\frac{2}{6}\) by dividing numerator and denominator by their greatest common divisor, which is 2.

After simplification, the reciprocal becomes \(\frac{1}{3}\), which is not equal to \(\frac{3}{1}\), so the statement is incorrect.

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Key Concepts

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

Reciprocal of a Number

The reciprocal of a number is obtained by swapping its numerator and denominator if it is a fraction. For example, the reciprocal of a/b is b/a. Multiplying a number by its reciprocal always results in 1.

Simplifying Fractions

Simplifying fractions involves reducing them to their lowest terms by dividing the numerator and denominator by their greatest common divisor. This makes it easier to compare or work with fractions.

Order of Operations and Fraction Interpretation

Understanding how to interpret expressions like 6/2 is crucial; it means 6 divided by 2, which equals 3. Recognizing this helps avoid errors when finding reciprocals or simplifying expressions.

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Textbook Question

Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. -3x^-1/3

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Textbook Question

Fill in the blank to correctly complete each sentence. In the term -6x²y, -6 is the ______.

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Textbook Question

Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. 3x^-1/3

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Textbook Question

Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. 3x^1/3

Textbook Question

Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. -3x^1/3

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Textbook Question

Determine whether each statement is true or false. If false, correct the right side of the equation. 5^-2 = 1/5²