Percent of change
Calculate percent of change in Grade 10 math using the formula (new-original)/original × 100%, distinguishing percent increase from percent decrease in real-world problems.
Key Concepts
$$\text{percent of change} = \frac{\text{amount of increase or decrease}}{\text{original amount}}$$ When the new amount is greater than the original, the change is a percent increase. When the new amount is less than the original amount, the change is a percent decrease.
From 150 to 180 is an increase. Percent change = $\frac{180 150}{150} = \frac{30}{150} = 0.2 = 20\%$ increase. From 20 to 17 is a decrease. Percent change = $\frac{20 17}{20} = \frac{3}{20} = 0.15 = 15\%$ decrease.
Think of this as a "change score" for numbers. We measure how much a value has grown or shrunk compared to where it started. It is like checking your video game score's jump from one level to the next, but we turn that fraction into a percentage to make it super easy to compare big changes!
Common Questions
What is the formula for percent of change?
Percent of change = (new value - original value) / original value × 100%. A positive result is a percent increase; negative is a percent decrease.
A price rises from $40 to $50. What is the percent increase?
(50-40)/40 × 100% = 10/40 × 100% = 25% increase.
A price drops from $80 to $60. What is the percent decrease?
(60-80)/80 × 100% = -20/80 × 100% = -25%, meaning a 25% decrease.