If $p = 15 - (3 - 5)$ and $q = (15 - 5) - 3,$ then $p - q =$

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Solution

First solve the given expressions for p, and q
$p = 15 - (3 - 5) \Rightarrow p = 15 - (- 2) \Rightarrow p = 15 + 2 \Rightarrow p = 17$

and $q = (15 - 5) - 3$
$\Rightarrow q = 10 - 3 \Rightarrow q = 7$

Clearly, changing the way of associating the numbers in subtraction changes the answer, as subtraction doesn’t have the associative property.

The value of p = 17 and q = 7

Now, subtract p - q
$∴ p - q = 17 - 7 = 10$

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