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 13

Chapter 1, Problem 13

Write each fraction in lowest terms. 18/90

Verified step by step guidance

Identify the numerator and denominator of the fraction: numerator = 18, denominator = 90.

Find the greatest common divisor (GCD) of 18 and 90. The GCD is the largest number that divides both 18 and 90 without leaving a remainder.

Divide both the numerator and the denominator by the GCD to simplify the fraction.

Write the simplified fraction as \(\frac{\text{numerator} \div \text{GCD}}{\text{denominator} \div \text{GCD}}\).

Verify that the fraction is in lowest terms by checking that the numerator and denominator have no common factors other than 1.

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Key Concepts

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

Simplifying Fractions

Simplifying fractions involves reducing the numerator and denominator to their smallest whole numbers while keeping the same value. This is done by dividing both by their greatest common divisor (GCD). The goal is to express the fraction in its simplest form.

Greatest Common Divisor (GCD)

The GCD of two numbers is the largest positive integer that divides both numbers without leaving a remainder. Finding the GCD is essential for simplifying fractions because it helps identify the factor by which both numerator and denominator can be divided.

Prime Factorization

Prime factorization breaks down a number into its prime number factors. This method helps in finding the GCD by identifying common prime factors between the numerator and denominator, making it easier to simplify the fraction.

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