7th Grade Math: Percent of Change and Percentages

Calculating Percent of Change

In percent of change problems, you're usually asked to figure out the percentage that an amount increases or decreases over time. For example, let's imagine that the average temperature last May was 80 degrees, and the average temperature last June was 90 degrees. What percent did the average temperature increase from May to June?

1. Find the absolute difference between the two amounts. In this example, 90 degrees - 80 degrees = 10 degrees.
2. Determine what percentage of the original amount the difference is. For instance, 10 degrees is 12.5% of 80, since 10/80 x 100 = 12.5.
3. Put the answer in the context of the problem. For this problem, the average temperature increased by 12.5% from May to June.

Tip: For percent decrease problems, you follow the same steps. You still report the percent decrease as a positive percentage, but you say that an amount decreased by x percent. The only exception to this rule is when you are displaying information in a table or chart. Since you can't provide a verbal explanation, you represent increases as positive percentages and decreases as negative percentages. For instance, a decrease of 2% would be written as -2% in a table.

Calculating Amount of Change

Some problems will tell you that an amount increased or decreased by a certain percentage. Then, they will ask you to determine the amount that this percentage represents. For instance, imagine that a school had 50 students starting kindergarten last year, but 10% fewer students started kindergarten this year. How many students started kindergarten this year?

1. Calculate the specified percentage of the original amount. In this case, you need to find 10% of 50. Since 50 x 10/100 = 500/100 = 5, five is 10% of 50.
2. Add or subtract that number to or from the original amount as necessary. In this problem, the number of students decreased by 10%, so you subtract five from 50 to get 45 (50 - 5 = 45). If this were a percent increase problem, you would add to the original amount.
3. State your answer in the terms of the problem. For this problem, you would say that 45 students started kindergarten this year.

Percentage Points

Sometimes, you'll be asked how many percentage points something increased or decreased by. For instance, if your science grade was 80% last week, and it's 87% this week, that means your grade increased by seven percentage points because 87 - 80 = 7. However, your grade did not increase by 7%, because the difference between your current grade and last week's grade is not equal to 7% of last week's grade.

Practice Problems

1. Ellen sold 15 tickets for the school dance last week, and this week she sold 30 tickets. By what percentage have her ticket sales increased since last week?

2. The first time Ray took his math test, he got just 40/80 questions correct. After studying some more, Ray retook the test and got 60/80 questions correct. The number of questions he got right increased by what percentage?

3. Last year, 60 students were in the school band, but this year, only 50 students are in it. By what percentage did the number of students in the school band decrease since last year?

Solutions

1. First, calculate the difference between 30 and 15, which is 15 (30 - 15 = 15). Next, divide 15 (the difference in the number of tickets sold) by 15 (the number of tickets sold last week). Since 15/15 = 1, and 1 x 100 = 100, Ellen's ticket sales increased by 100% since last week.

2. The difference in the number of questions Ray got correct between his first test and his second test is 20, since 60 - 40 = 20. To calculate the percent increase, divide 20 by Ray's first score of 40 questions correct to get 0.5 (20/40 = 1/2 = 0.5). The decimal 0.5 x 100 = 50, so the number of questions Ray got correct increased by 50%.

3. The difference in the number of students in the school band between this year and last year is ten, because 60 - 50 = 10. The fraction 10/50 = 1/5 = 0.2, and 0.2 x 100 = 20. This means that the number of students in the school band decreased by 20% between this year and last year.