Reduce fractions to lowest terms

Learning Objectives Identify the Greatest Common Divisor (GCD) of the numerator and denominator in a fraction representing an angle ratio. Reduce trigonometric ratios (sin, cos, tan) to their simplest form. Express the measure of an angle as a simplified fraction of a full circle (360°) or a straight line (180°). Simplify the fractional part of a radian measure when converting from degrees. Apply fraction reduction to solve problems involving similar triangles and angle properties. Verify that a fraction is in its lowest terms by confirming the GCD of the numerator and denominator is 1. If a pizza is cut into 12 slices and you eat 8, what's the simplest way to describe the fraction of the pizza you ate? 🍕 This same skill is crucial for understanding angles! This tutor...

TermDefinitionExample Lowest TermsA fraction is in lowest terms (or simplest form) when its numerator and denominator have no common factors other than 1. Their Greatest Common Divisor (GCD) is 1.The fraction 8/12 is not in lowest terms. By dividing both the numerator and denominator by their GCD of 4, we get 2/3, which is in lowest terms. Greatest Common Divisor (GCD)The largest positive integer that divides two or more integers without leaving a remainder. It's also known as the Greatest Common Factor (GCF).For the numbers 24 and 36, the common divisors are 1, 2, 3, 4, 6, and 12. The Greatest Common Divisor is 12. RatioA comparison of two quantities, often expressed as a fraction. In geometry, we often compare lengths of sides or measures of angles.In a right triangle, the ratio of...

The Fundamental Rule of Fraction Reduction \frac{a}{b} = \frac{a \div \text{GCD}(a, b)}{b \div \text{GCD}(a, b)} To reduce any fraction to its lowest terms, find the Greatest Common Divisor (GCD) of the numerator (a) and the denominator (b). Then, divide both the numerator and the denominator by their GCD. Tangent Ratio Definition \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} In a right triangle, the tangent of an angle (θ) is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. This ratio must be simplified.