Here are two ways to calculate a percentage change, use the one you prefer:
Method 1<span>Step 1: Calculate the change (subtract old value from the new value)Step 2: Divide that change by the old value (you will get a decimal number)Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign) Note: when the new value is greater then the old value, it is a percentage increase, otherwise it is a decrease.</span>Method 2<span>Step 1: Divide the New Value by the Old Value (you will get a decimal number)Step 2: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)Step 3: Subtract 100% from that Note: when the result is positive it is a percentage increase, if negative, just remove the minus sign and call it a decrease.</span>ExamplesExample: A pair of socks went from $5 to $6, what is the percentage change?
Answer (Method 1):
<span>Step 1: $5 to $6 is a $1 increaseStep 2: Divide by the old value: $1/$5 = 0.2<span>Step 3: Convert 0.2 to percentage: 0.2×100 = 20% rise.</span></span>
Answer (Method 2):
<span>Step 1: Divide new value by old value: $6/$5 = 1.2Step 2: Convert to percentage: 1.2×100 = 120% (i.e. $6 is 120% of $5)<span>Step 3: Subtract 100%: 120% - 100% = 20%, and that means a 20% rise.</span></span>
Another Example: There were 160 smarties in the box yesterday, but now there are 116, what is the percentage change?
Answer (Method 1): 160 to 116 is a decrease of 44. Compared to yesterday's value: 44/160 = 0.275 = 27.5% decrease.
Answer (Method 2): Compare today's value with yesterday's value: 116/160 = 0.725 = 72.5%, so the new value is 72.5% of the old value.
Subtract 100% and you get -27.5%, or a 27.5% decrease.
Why Compare to Old Value?
Because you are saying how much a value has changed.
Example: Milk was $2, now it is $3, did it rise $1 compared to $2 or $3 ?
We compare to the original $2 value, so we say the change is $1/$2 = 0.5 which is a <span>50% increase</span>
. And the correct answer is D).