Distributive property without variables

Students will learn how to use the distributive property to evaluate expressions. The distributive property works because multiplication is repeated addition. Consider that \(2 \cdot 3 + 2 \cdot 4\) is the sum of 3 2's and 4 2's, which is the same as 3 + 4 2's. Mathematically, \(2 \cdot 3 + 2 \cdot 4 = 2(3 + 4).\) Students will also use the distributive property to mentally evaluate certain expressions. For example, when looking at \(16 \cdot 43 + 16 \cdot 57,\) I don't want to figure out \(16 \cdot 43,\) nor \(16 \cdot 57.\) But I notice that \(43 + 57 = 100,\) so mentally I replace \(16 \cdot 43 + 16 \cdot 57\) with \(16 \cdot 100,\) which is obviously \(1{,}600.\) Thus, my original expression \(16 \cdot 43 + 16 \cdot 57\) must be equal to \(1{,}600.\) As another example, suppose I want to know \(9 \cdot 16.\) This isn't something I know off the top of my head, so I mentally replace this with \(9 \cdot 10 + 9 \cdot 6.\) That's \(90 + 54,\) I think to myself. And \(90 + 54 = 144.\) Thus, my original expression, \(9 \cdot 16,\) must be equal to \(144.\)