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 6

Chapter 1, Problem 6

Which fraction is not equal to 5/9? A. 15/27 B. 30/54 C. 40/74 D. 55/99

Verified step by step guidance

Understand that two fractions are equal if their cross products are equal or if one fraction can be simplified to the other.

Check each option by simplifying the fraction or by cross-multiplying to compare it with \(\frac{5}{9}\).

For option A, compare \(\frac{15}{27}\) with \(\frac{5}{9}\) by simplifying \(\frac{15}{27}\): divide numerator and denominator by their greatest common divisor.

For option B, do the same: simplify \(\frac{30}{54}\) or cross-multiply to check equality with \(\frac{5}{9}\).

For options C and D, repeat the process: simplify or cross-multiply to verify if they are equal to \(\frac{5}{9}\). The fraction that does not simplify to \(\frac{5}{9}\) is the answer.

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Key Concepts

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

Equivalent Fractions

Equivalent fractions represent the same value or proportion, even if their numerators and denominators differ. They can be found by multiplying or dividing both numerator and denominator of a fraction by the same nonzero number.

Simplifying Fractions

Simplifying a fraction involves dividing the numerator and denominator by their greatest common divisor (GCD) to reduce it to its simplest form. This helps in easily comparing fractions to determine equivalence.

Cross Multiplication

Cross multiplication is a method to compare two fractions by multiplying the numerator of each fraction by the denominator of the other. If the cross products are equal, the fractions are equivalent.

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