Examples of simplifying probability fractions with solutions.

🧮 Quick Study Guide

• 🔍 Probability Basics: Probability is the measure of the likelihood that an event will occur. It's expressed as a fraction, decimal, or percentage.
• ➗ Simplifying Fractions: Simplifying a fraction means reducing it to its lowest terms. To do this, find the greatest common divisor (GCD) of the numerator and denominator and divide both by it.
• ➗ Simplifying Probability Fractions: The probability of an event happening is often expressed as a fraction: $\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$. This fraction can often be simplified.
• ➗ Finding the GCD: The GCD is the largest number that divides both the numerator and denominator without leaving a remainder. Common methods to find GCD include listing factors or using the Euclidean algorithm.
• 💡 Example: Consider the probability fraction $\frac{6}{12}$. The GCD of 6 and 12 is 6. Dividing both numerator and denominator by 6 gives $\frac{6 \div 6}{12 \div 6} = \frac{1}{2}$.
• 💯 Expressing in Simplest Form: A probability fraction is in its simplest form when the numerator and denominator have no common factors other than 1.

✍️ Practice Quiz

1. Question 1: What is the simplified form of the probability fraction $\frac{4}{16}$?
   1. A) $\frac{1}{2}$
   2. B) $\frac{1}{4}$
   3. C) $\frac{2}{8}$
   4. D) $\frac{4}{4}$
2. Question 2: Simplify the probability fraction $\frac{10}{25}$.
   1. A) $\frac{1}{5}$
   2. B) $\frac{2}{5}$
   3. C) $\frac{5}{5}$
   4. D) $\frac{10}{5}$
3. Question 3: What is the simplified form of $\frac{12}{18}$?
   1. A) $\frac{2}{3}$
   2. B) $\frac{3}{2}$
   3. C) $\frac{4}{6}$
   4. D) $\frac{6}{9}$
4. Question 4: Simplify the probability fraction $\frac{8}{20}$.
   1. A) $\frac{2}{4}$
   2. B) $\frac{2}{5}$
   3. C) $\frac{4}{5}$
   4. D) $\frac{1}{2}$
5. Question 5: What is the simplified form of $\frac{15}{45}$?
   1. A) $\frac{1}{2}$
   2. B) $\frac{1}{3}$
   3. C) $\frac{5}{15}$
   4. D) $\frac{3}{9}$
6. Question 6: Simplify the probability fraction $\frac{9}{21}$.
   1. A) $\frac{1}{3}$
   2. B) $\frac{3}{7}$
   3. C) $\frac{3}{3}$
   4. D) $\frac{9}{7}$
7. Question 7: What is the simplified form of $\frac{20}{30}$?
   1. A) $\frac{2}{3}$
   2. B) $\frac{4}{6}$
   3. C) $\frac{10}{15}$
   4. D) $\frac{1}{2}$