Percent of change

key notes :

Percent of Change 📊✨

What is Percent of Change? 🤔

  • It tells us how much a quantity has increased or decreased in terms of percent.
  • Example: Prices go up 💰 or down ⬇️, population grows 🌱, scores change 🏆.

    Types of Change 🔄

    • Percent Increase 📈: When the new value is more than the original value.
    • Percent Decrease 📉: When the new value is less than the original value.

      Formula for Percent of Change 📝

        Percent of Change = New Value – Original Value / Original Value×100

        • If result is positive ➕, it’s a percent increase.
        • If result is negative ➖, it’s a percent decrease.

        Step by Step Method 🧩

        1. Find the difference: New Value – Original Value
        2. Divide the difference by the Original Value
        3. Multiply by 100 to get the percent
        4. Add % sign ✅

          Quick Tips ⚡

          • Always compare to the original value, not the new value.
          • Use a positive sign for increase and negative for decrease.
          • Check your answer: percent cannot exceed 100% in normal cases unless it doubles or more.

            Examples 🧮

            • Original price: ₹200 → New price: ₹250

            \text{Percent Increase} = \frac{250-200}{200} \times 100 = 25\% \] ✅

            • Original marks: 80 → New marks: 60

            \text{Percent Decrease} = \frac{60-80}{80} \times 100 = -25\% \] ✅

              Emojis to Remember 😎

              • 📈 = Increase
              • 📉 = Decrease
              • 💯 = Percent
              • ✨ = Important formula

                Learn with an example

                What is the percent of change from 7,000 to 700?

                • 1.) 84% decrease
                • 2.)90% increase
                • 3.) 90% decrease
                • 4.) 84% increase

                Plug 7,000 and 700 into the formula for percent of change and simplify.

                percent of change= amount of change/original amount

                =7000-700/7000

                =6300/7000

                =0.9

                Write the number as a percent.

                0.9 → 90%

                Finally, figure out whether the percent of change is an increase or decrease. Since the number goes down from 7,000 to 700, it is a decrease.

                The percent of change is a 90% decrease.

                What is the percent of change from 14 to 21?

                • 1.) 50% increase
                • 2.) 52% increase
                • 3.) 50% decrease
                • 4.) 52% decrease

                Plug 14 and 21 into the formula for percent of change and simplify.

                percent of change= amount of change/original amount

                =21-14/14

                =7/14

                =0.5

                Write the number as a percent.

                0.5 → 50%

                Finally, figure out whether the percent of change is an increase or decrease. Since the number goes up from 14 to 21, it is an increase.

                The percent of change is a 50% increase.

                What is the percent of change from 80 to 16?

                • 1) 80% decreases
                • 2) 80% increases
                • 3) 76% increases
                • 4) 76% decreases

                Plug 80 and 16 into the formula for percent of change and simplify.

                percent of change= amount of change/original amount

                =80-16/16

                =64/16

                =0.8

                Write the number as a percent.

                0.8 → 80%

                Finally, figure out whether the percent of change is an increase or decrease. Since the number goes down from 80 to 16, it is a decrease.

                The percent of change is an 80% decrease.

                let’s practice!