### Learning Outcomes

By the end of this section, you will be able to:

- Given a ratio of two integers, write it as a fraction.
- Given a ratio of two decimals, write it as a fraction.
- Given a ratio of two mixed numbers, write it as a fraction.
- Use a model to find the sum of two fractions with the same denominator.
- Add fractions with a common denominator without a model.
- Use fraction circles to find the difference between two fractions with like denominators.
- Subtract fractions with a like denominator without fraction circles.
- Find the least common multiple of two numbers by listing multiples.
- Find the least common multiple of two numbers by prime factorization
- Add or subtract fractions with different denominators.
- Identify and use fraction operations.
- Find the probability of an event given the number of favorable outcomes and the total number of outcomes possible

The study of probability may be thought of as a study of random outcomes or risk. Probability is useful in analyzing games of chance, business risk, market analysis, life insurance, finance, government policy planning, and scientific studies, to name a few. While it is a relatively young field in mathematics, its applications are far reaching into nearly every aspect of human life. Probability, like statistics, has its own particular language of terms and symbols that you’ll need to spend time with in this module. Much of the mathematics of probability involves fractions, which you have studied in previous sections. Nevertheless, it will be good to spend some time preparing for this module with a review of ratios and arithmetic on fractions, particularly with regard to adding and subtracting fractions. Since it is often desirable to view probabilities in fraction form rather than converting to decimals to compute them, you’ll also see a technique for finding the least common multiple involving prime factorizations that may prove useful. We’ll end the review module with a preview of finding the probability of an event to help you practice fractions in context.

### Recall for success

Look for red boxes like this one throughout the text. They’ll show up just in time to give helpfulĀ reminders of the math you’ll need, right where you’ll need it.