Percent of change: word problems
key notes :
🔢 What is Percent of Change?
Percent of change tells us how much a value increases or decreases compared to the original amount.
It includes:
- Percent Increase 📈
- Percent Decrease 📉
🧮 Formula to Find Percent of Change
✔️ Percent of Change =
New Value – Original Value / Original Value × 100
🔹 If the answer is positive → Percent Increase
🔹 If the answer is negative → Percent Decrease
📈 Percent Increase
Used when the value goes up.
Example:
A book cost ₹200 and now costs ₹250.
Increase = 250 − 200 = 50
Percent increase = 50 / 200 × 100 = 25% 🎉
📉 Percent Decrease
Used when the value goes down.
Example:
A shirt price was ₹500 and now it is ₹400.
Decrease = 500 − 400 = 100
Percent decrease = 100 / 500 × 100 = 20% 🪙
🏁 Steps to Solve Word Problems
Step 1: Identify original value and new value 🧐
Step 2: Find the difference (increase or decrease)
Step 3: Use the percent of change formula
Step 4: Label answer as increase or decrease
💡 Keywords to Watch in Word Problems
- Increased by
- Decreased by
- Discount
- Marked up
- Reduced to
- Profit/Loss
- Grew/Shrank
🧠 Tips to Remember
✨ Always divide by the original value
✨ Round answers to the nearest whole number when needed
✨ Use units like % increase or % decrease
Learn with an example
😀 Toby enjoys taking part in races and keeps track of all of his finishing times. At a race last month, he finished in 350 minutes. Yesterday, he completed another race and finished in 315 minutes. What is the decrease in Toby’s finishing time?——%.
Plug 350 minutes and 315 minutes into the formula for percent of change and simplify.
percent of change=amount of change/original amount
=350-315/350
=35/350
=0.1
Write the number as a percent.
0.1–>10%
The percent of decrease in Toby’s finishing time is 10%.
😀 A mountain on a tropical island experiences changes in height due to volcanic activity. When the mountain was last measured, its height was 2,820 metres. Now is 3,384 metres. What is the percent of increase in the height of the mountain?——%.
Plug 2,820 metres and 3,384 metres into the formula for percent of change and simplify.
percent of change=amount of change/original amount
=3384-2820/2820
=564/2820
=0.2
Write the number as a percent.
0.2–>20%
The percent of increase in the height of the mountain is 20%.
😀 During summer holiday, Dorothy read, on average, 35 pages per night. Once she returned to school, she averaged 7 pages per night. What is the percent of decrease in Dorothy’s reading?—–%.
Plug 35 pages and 7 pages into the formula for percent of change and simplify.
percent of change=amount of change/original amount
=35-7/35
=28/35
=0.8
Write the number as a percent.
0.8–>80%
The percent of decrease in Dorothy’s reading is 80%.
let’s practice!
