MathCastle
Groups and FieldsEasyGroups and the Group Axioms

Groups and the Group Axioms · Easy problem

Define a∗b=a+b2a*b=\dfrac{a+b}{2} for real numbers a,ba,b. Compute (2∗6)∗10(2*6)*10 and 2∗(6∗10)2*(6*10), and find by how much they differ.