Why is it recommended not to simplify fractions until the end when solving the inclusion-exclusion equation?

Conditions

• All probability terms in the equation share the same denominator.

Reasoning, step by step

1. Identify that all fractions in the equation have the same denominator.
2. Perform addition and subtraction directly on the numerators while keeping the denominator unchanged.
3. Isolate the unknown term.
4. Simplify the final resulting fraction to its lowest terms.

Example

In the example, the equation $25/30 = 18/30 + 15/30 - P(L \cap D)$ is solved by combining $18/30$ and $15/30$ into $33/30$, avoiding the need to convert $25/30$ to $5/6$ early.

Common misconceptions

• Thinking that simplifying fractions at every step is always the best mathematical practice.
• Forgetting that reducing a fraction changes its denominator, making it harder to combine with other terms.

Watch the explanation

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