Direct product of spin representations Consider a system of two 1/2-spins. Under some conditions the Hilbert space can be decomposed into the direct sum of spin-0 and spin-1 representations:
$\frac12\otimes\frac12=0\oplus1$. 
When I write this formula on the board, I immediately get an objection that $1/4$ is not equal to 1 ! My question is as follows, how to explain this equation to the audience of physicists. Preferably in one or two sentences, concise, mathematically correct, but without going into much mathematical details. 
 A: Each spin-1/2 particle is associated with a $(2\times\frac{1}{2}+1)$=2-dimensional vector space $\mathbb{V}$ as far as its spin degree of freedom is concerned. A composite system of two spin-1/2 particles is associated with a 4-dimensional vector space which is a direct product $\mathbb{V}_1\otimes \mathbb{V}_2$ of two 2-dimensional vector spaces $\mathbb{V}_1$ and $\mathbb{V}_2$. Under a similarity transformation a $4\times 4$ matrix representing an element of $SU(2)$ that acts on the space $\mathbb{V}_1\otimes \mathbb{V}_2$, can be reduced to a block-diagonal form consisting of block matrices of dimensions $3\times 3$ and $1\times 1$ acting on invariant subspaces of dimensions 3 and 1 respectively. 
In technical terms, it means that the 4-dimensional representation is reducible into a 3-dimensional and 1-dimensional irreducible representations, and symbolically written as $2\otimes 2=3\oplus 1$ which respectively corresponds to three triplet states of spin-1 and one singlet state of spin-0 of the composite system.
