GED Mathematical Reasoning: Percent Change (Increase/Decrease)

  • Percent of change, whether the change is an increase or decrease, is a comparison of two numbers: the amount of change and the original amount.
  • Calculating the percent of increase or decrease involves using a very simple formula: the amount of change divided by the original amount.

Percent\, of\, Change = \frac{Amount\, of\, Change}{Original\, Amount}

  • The amount of change is the difference between the new number and the original amount. And always subtract the smaller number from the larger number.
  • So finding percent of change is a two step process. First, we must find the amount of change using subtraction, taking care to subtract the smaller number from the larger number. Second, we’ll divide that difference by the original amount.

 

Example 1

Last month, Belinda’s retirement savings account was worth $35,400. This month, it is worth $36,816. By what percent did Belinda’s retirement account increase?

 

Let’s write down the information we’re given. We’re told that Belinda’s retirement account went from being worth $35,400 to being worth $36,816.

Now let’s talk about our plan of action. Because we’re being asked to find the percent of increase, we’ll use the formula for percent of change.

To execute our plan, we first need to calculate the amount of change. Since Belinda’s retirement account went from being worth $35,400 to being worth $36,816, the amount of change can be found by subtracting these two amounts. And we’ll be careful to subtract the smaller number from the larger number.

Amount of Change = $36,816 – $35,400 = $1,416

For the second step, we’ll divide the amount of change by the original amount, which was $35,400.

Percent\, of\, Change = \frac{\$1416}{\$35400} = 0.04

Notice that the percent of change calculation gives us a result in decimal form. We can easily change this decimal to a percent, though, by moving the decimal point two places to the right, making the final answer 4%.

0.04 \rightarrow 4\%

Does this answer make sense? Although Belinda’s retirement account did grow, it didn’t grow very much. So we wouldn’t expect the percent of increase to be terribly high. So yes, a percent increase of 4% makes sense.

 

Example 2

Today, 2106 people attended the county fair. Yesterday, 3900 people attended the fair. What was the percent decrease in attendance from yesterday to today?

 

We’re given two attendance numbers for the county fair. Yesterday the attendance was 3900. Today, it was 2106. We can use the percent of change formula no matter if there is an increase or decrease.

The first step in using the percent of change formula is to find the amount of change. Remember to subtract the smaller number from the larger number.

Amount of Change = 3900 – 2106 = 1794

For the second step, we’ll divide the amount of change by the original amount. Don’t let the way the problem is worded fool you. Although the number 2106 is given FIRST, the original amount is actually 3900, since yesterday comes before today.

Percent\, of\, Change = \frac{1794}{3900} = 0.46

0.46 written as a decimal is 46%

0.46 \rightarrow 46\%

Does it make sense? 2106 can be rounded down to 2000 and 3900 can be rounded up to 4000. And using these rounded numbers, we can more easily see that the attendance dropped by about half or 50%. So yes, 46% is a reasonable answer.

By the way, here’s another way to check your work:

Attendance dropped by 46%, so today’s attendance should be 54% of yesterday’s attendance, since 46% + 54% = 100%. The word “of” implies multiplication, so to find 54% of 3900, multiply 0.54 [read: point five four] times 3900. When we do so, the result is today’s attendance: 2106, as it should be.

 

Example 3

Suppose a chicken farmer started with a flock of 20 chickens and now has 200 chickens. Find the percent of increase.

 

Be aware that percent of increase may be greater than 100%. The amount of change, in this case, is 180 chickens since 200 minus 20 equals 180.

Amount of Change = 200 – 20 = 180

When we divide the amount of change by the original amount of 20, the result is 9.

Percent of Change = \frac{180}{20} = 9

Although we don’t see a decimal point here, we assume it is located to the right of the 9. When we move that decimal point two places to the right and add a place-holding zero, the result is 900%. So the chicken farmer has experienced a 900% increase in his flock.

9.0 \rightarrow 900\%

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