Maintaining Mathematical Proficiency
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Think of a numerical expression that involves both addition and multiplication.
See solution.
We are asked to give an example to show why the order of operations is important when evaluating a numerical expression. Then, we are also asked if the order of transformations of figures is important. Let's discuss these things one at a time.
The order of transformations of figures is also important. Consider a triangle whose vertices are A(1,1), B(3,3), and C(1,5).
Let's translate the above triangle 4 units to the right and 1 unit up, and then reflect it in the x-axis.
We see that the resulting triangle has vertices (5,- 2), (7, - 4), and (5,- 6). Let's now apply the same transformations but in a different order. We will reflect △ABC in the x-axis, and then translate 4 units to the right and 1 unit up.
We see that the resulting triangle has vertices (5,0), (7,- 2), and (5, - 4). Therefore, we do not obtain the same result if we do not follow the same order of transformations.