Error Analysis
Students were asked to solve the equation for m. Their work is shown below. Which student solved the equation correctly? Why did the other 2 students sol the equation incorrectly?
(3 + n)/m = b Solve for m.
Student 1 (3 + n)/m = b 3 + n = bm n = bm - 3 n/b = m - 3 n/b + 3 = m m = n/b + 3
Student 2 (3 + n)/m = b 3 + n = bm (3 + n)/b = m m = (3 + n)/b
Student 3 (3 + n)/m = b n/m = b - 3 m = n/(b - 3)
Student 3 solved the equation correctly. They correctly isolated the variable m on one side of the equation by dividing both sides by (3 + n) to get n/m = b - 3, and then they solved for m by taking the reciprocal of both sides to get m = n/(b - 3).
Student 1 made an error when they subtracted 3 from both sides of the equation. This mistake led to the incorrect equation n/b + 3 = m. They should have divided both sides by b to isolate m.
Student 2 made an error when they multiplied both sides of the equation by b. This mistake led to the incorrect equation (3 + n)/b = m. They should have divided both sides by b to isolate m.