Three concepts help explain the process of simplifying fractions:

1. Multiplying a quantity by 1 has no effect

2. A fraction whose numerator is exactly the same as its denominator is equal to 1 (unless the denominator equals zero)

3. A product of two fractions can be rewritten as a fraction of two products (and vice versa)

To simplify a fraction:

- Rewrite both numerator and denominator as products of factors (if they are not already factored)
- Examine both numerator and denominator to see if they share any factors
- If they do share factors, use concept (3) above to move the shared factors into a separate fraction
- That separate fraction should now have a numerator that is exactly the same as its denominator, which by concept (2) above means that it must equal 1, therefore by concept (1) above we can drop it from the expression

Consider the following fraction… can it be simplified?

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