Discussion
Let a, b, c be three rational numbers, where \(a = \frac{3}{5}\), \(b = \frac{2}{3}\) and \(c = \frac{-5}{6}\). Which one of the following is true?
Answer: C
The true statement is a + (b + c) = c + (a + b).
Addition of rational numbers is both associative and commutative, so the three numbers can be added in any grouping and any order and the sum is the same: both sides equal a + b + c. With the given values,
\[ \begin{aligned} \tfrac{3}{5} + \tfrac{2}{3} - \tfrac{5}{6} &= \tfrac{18 + 20 - 25}{30} \\ &= \tfrac{13}{30} \end{aligned} \]
on both sides. The other statements fail because multiplication, division and subtraction do not let you swap the numbers like this: for example a × (b + c) = (3/5)(−1/6) = −1/10, but b × (a + c) = (2/3)(−7/30) = −7/45.
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