Percent Change, Reverse Percentages, and Successive Changes

Objective: Compute an increase or decrease relative to the original.

Prerequisite skills: percent factors and linear equations. Percent change is the difference divided by the original amount, times 100%. The direction comes from whether the final amount is larger or smaller. Do not divide by the final amount unless a different comparison is requested. Common error: using the final amount as the percent base. Restrictions and interpretation: Percent change uses the original amount as its denominator; reverse a percent by division.

Objective: Recover an original amount from a changed amount.

If the final amount is a known factor times the original, divide by that factor. Subtracting the stated percentage of the final amount uses the wrong base and does not undo the change. Common error: subtracting the growth percentage from the final amount. Restrictions and interpretation: Percent change uses the original amount as its denominator; reverse a percent by division.

Objective: Compute one net percent from a product of factors.

Multiply all change factors to get the overall final-to-original ratio. Subtract 1 and multiply by 100 to express the net percent change. A positive result is an increase and a negative result a decrease. Common error: adding the rates instead of multiplying the factors. Restrictions and interpretation: Percent change uses the original amount as its denominator; reverse a percent by division. Desmos and method choice: Use Desmos for arithmetic or a graph/table check when that reduces work. Enter parentheses explicitly and verify the requested quantity and units. Use the algebraic steps shown here for an exact result; a rounded graph display is not proof of exact equality.