Percent of change: word problems

Learning Objectives Identify the original and new amounts in a word problem. Calculate the absolute amount of change between two values. Apply the percent of change formula to solve real-world problems. Distinguish between percent increase and percent decrease. Interpret the meaning of a calculated percent of change in context. Solve multi-step word problems involving percent of change. Ever wonder how much a store's prices went up or down? 📈📉 Or how much a population grew? Let's find out how to measure these changes! In this lesson, you'll learn how to calculate the 'percent of change,' which tells us how much a quantity has increased or decreased relative to its original size. This skill is super useful for understanding real-world data, from fi...

TermDefinitionExample Original AmountThe starting value or initial quantity before any change occurs.If a shirt cost $20 last week and now costs $25, the original amount is $20. New AmountThe final value or quantity after a change has occurred.If a shirt cost $20 last week and now costs $25, the new amount is $25. Amount of ChangeThe absolute difference between the new amount and the original amount. It's always a positive value.If a shirt changed from $20 to $25, the amount of change is $25 - $20 = $5. Percent of ChangeA ratio that expresses the amount of change as a percentage of the original amount. It tells us the relative size of the change.A $5 change on an original $20 item is a (5/20)*100% = 25% change. Percent IncreaseThe percent of change when the new amount is greater than...

Amount of Change Formula $$\text{Amount of Change} = |\text{New Amount} - \text{Original Amount}|$$ Use this to find the absolute difference between the two values. The absolute value ensures the result is always positive. Percent of Change Formula $$\text{Percent of Change} = \frac{\text{Amount of Change}}{\text{Original Amount}} \times 100\%$$ This is the primary formula for calculating any percent of change. Remember to divide by the *original* amount and multiply by 100% to express as a percentage. Percent Increase Formula $$\text{Percent Increase} = \frac{\text{New Amount} - \text{Original Amount}}{\text{Original Amount}} \times 100\%$$ Specifically used when the quantity has grown. The numerator will be positive. Percent Decrease Formula $$\text{Percent D...