Write each fraction in lowest terms. 16/20

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Identify the numerator and denominator of the fraction: numerator = 16, denominator = 20.

Find the greatest common divisor (GCD) of 16 and 20. The GCD is the largest number that divides both 16 and 20 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 divisors other than 1.

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Key Concepts

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

Greatest Common Divisor (GCD)

The Greatest Common Divisor is the largest positive integer that divides two numbers without leaving a remainder. Finding the GCD of the numerator and denominator helps simplify fractions by reducing them to their lowest terms.

Simplifying Fractions

Simplifying a fraction involves dividing both the numerator and denominator by their GCD to create an equivalent fraction with smaller numbers. This process makes the fraction easier to understand and work with.

Equivalent Fractions

Equivalent fractions represent the same value even though they have different numerators and denominators. Simplifying fractions produces an equivalent fraction in lowest terms, which is the simplest form of the fraction.

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Work each problem. Which of the following is the correct factorization of x³+8?

A. (x+2)³

B. (x+2)(x²+2x+4)

C. (x+2)(x²-2x+4)