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What's a Percent of Change?

Formula: Percent of Change

Summary

  1. Percent of change is the percent that value increases or decreases by
  2. The vertical bars are the symbols for absolute value
  3. The amount of change is equal to the absolute value of the new amount minus the old amount
  4. The '>' symbol means 'greater than'
  5. If the new value is greater than the old value, we have a percent of increase
  6. The '<' symbol means 'less than'
  7. If the new value is less than the old value, we have a percent of decrease

Notes

    1. The amount of change is the difference between the two amounts
    1. This gives a proportion we can solve to find percent of change
    1. The absolute value of the difference of two numbers is the distance they are from each other on a number line
    2. Since distances are always positive, absolute value is always positive
    3. The vertical bars on either side of the subtraction are the symbols for absolute value
    4. To find absolute value, subtract the two numbers and then make that value positive
    1. If the new amount is bigger than the old amount, then its value has increased
    1. If the new amount is smaller than the old amount, then its value has decreased
    1. $10 is the old price
    2. $15 is the new price
    1. The amount of change is the absolute value of difference between the old amount and the new amount
    1. Subtract 10 from 15 and put this subtraction inside the vertical bars that symbolize absolute value
    1. We need to find the absolute value of 15-10
    2. 15-10 is 5
    3. Since 5 is already positive, we leave it positive
    4. So the absolute value of 15-10 is 5
    1. Now we can solve this proportion for our unknown, the percent of change
    1. To cross-multiply:
    2. Multiply 10 by the percent of change and put that on the left hand side
    3. Then multiply 5•100 and put that product on the right hand side
    4. 5•100=500 on the right hand side
    1. Division is the opposite of multiplication
    2. So we can divide both sides by 10 to get the percent of change by itself
    1. The 10's cancel on the left
    2. 500/10=50 on the right
    3. So our percent of change is 50
    1. We need to compare the new amount to the old amount and see which one is bigger
    2. If the new amount is bigger, we have a percent of increase
    3. If the old amount is bigger, we have a percent of decrease
    1. The price went from $10 to $15, so its value increased
    2. The '>' symbol means 'greater than'
    3. So we have a percent of increase