Video: Calculating the Percentage That Describes a Change in Quantity and Finding Whether It Is an Increase or Decrease

Determine, to the nearest whole percent, the percent of change of $186.40 to $235. State whether it is an increase or a decrease.

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Video Transcript

Determine, to the nearest whole percent, the percent of change of 186 dollars and 40 cents to 235 dollars. State whether it is an increase or a decrease.

A percentage of change is equal to the amount of change divided by the original amount multiplied by 100. The first part of this calculation gives a proportion of the original amount that the change represents. The second part converts this from a decimal to a percentage. Let’s look at the values in this question.

The original, or starting, amount is equal to 186 dollars and 40 cents. The amount of change is equal to 235 dollars minus 186 dollars and 40 cents, which is 48 dollars and 60 cents. Now, let’s substitute these values into the formula. The percent of change is equal to 48 dollars and 60 cents divided by 186 dollars and 40 cents multiplied by 100.

The question states that our answer should be given to the nearest whole percent. We’ll suggest we can use a calculator to evaluate this. It’s equal to 26.072961. Rounded to the nearest whole percent, this is equal to 26 percent.

The second part of the question is actually more straightforward. It asked whether this is an increase or a decrease. Well, as the change is from 186 dollars and 40 cents to 235 dollars, this is an increase.

Now, there is one commonly-made error that you need to watch out for. Remember, in the formula for percent of change, we need to divide by the original amount. The common error is to accidentally divide by the new amount instead. In this question, this will give a calculation of 48.60 divided by 235 multiplied by 100. And to the nearest whole percent, this would be 21 percent. This is an incorrect answer. But if you did get 21 percent yourself, then this is where you’re going wrong.

Remember, when calculating a percent of change, we always divide by the original amount.

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