1. **Stating the problem:** We want to understand the properties of addition illustrated by the expressions: $b + c = d$ $b + (c + d) = (b + c) + d$ $b + c = c + d$ $b + c = c + b$ 2. **Relevant properties of addition:** - **Associative property:** $a + (b + c) = (a + b) + c$ - **Commutative property:** $a + b = b + a$ 3. **Analyzing each expression:** - $b + c = d$ defines $d$ as the sum of $b$ and $c$. - $b + (c + d) = (b + c) + d$ shows the associative property. - $b + c = c + d$ is generally false unless $b=0$ because substituting $d = b + c$ gives $b + c = c + (b + c)$. - $b + c = c + b$ shows the commutative property. 4. **Final answer:** The expressions demonstrate that addition is associative and commutative, meaning the grouping and order of addition do not affect the sum.