To find the percentage change from 90 to 75, we need to first calculate the difference between the two numbers.

, we'll follow a step-by-step problem-solving approach.

**Step 1: Identify the original value and the new value. In this case, the original value is 90 and the new value is 75.**

**Step 2: Find the change in value. To determine the change, we subtract the new value from the original value. So, 90 minus 75 equals 15.**

**Step 3: Calculate the percent decrease. To find the percent decrease, we need to express the change as a percentage of the original value. We can use the following formula: Percent decrease = (change/original value) x 100**

Plugging in the values, we have: Percent decrease = (15/90) x 100

**Step 4: Simplify and calculate. To simplify the fraction, we can cancel out any common factors between the numerator (15) and the denominator (90). In this case, both 15 and 90 can be divided by 15, resulting in: Percent decrease = (1/6) x 100**

Now, let's calculate the percentage: Percent decrease = 1/6 x 100 = 16.67%

So, the percent decrease from 90 to 75 is 16.67%. This means that the value has decreased by approximately 16.67% from the original value of 90 to the new value of 75.

When calculating percentages, it's essential to understand the relationship between the original and new values.

By following this step-by-step approach, we can accurately determine the percent decrease between any two values.

Let’s try to look at some examples:

**Example 1:** Clothing Sale

A clothing store offers a sale with a 30% discount on all items. If a pair of jeans originally costs $50, what is the new price after the discount?

To find the new price after the discount, we need to calculate the amount of the discount and subtract it from the original price.

Step 1: Calculate the amount of the discount.

30% of $50 can be found by multiplying 0.30 by $50:

Discount = 0.30 × $50 = $15.

Step 2: Subtract the discount from the original price.

New price = $50 - $15 = $35.

Therefore, after the 30% discount, the new price of the jeans is $35.

**Example 2:** Stock Market Performance

A company's stock was trading at $100 per share at the beginning of the year. By the end of the year, the stock price had decreased to $80 per share. What is the percent decrease in the stock price?

To find the percent decrease, we'll follow the step-by-step approach we discussed earlier.

Step 1: Identify the original value and the new value.

The original value is $100, and the new value is $80.

Step 2: Find the change in value.

Change = Original value - New value = $100 - $80 = $20.

Step 3: Calculate the percent decrease.

Percent decrease = (Change/Original value) × 100 = ($20/$100) × 100 = 20%.

Therefore, the stock price experienced a 20% decrease from the beginning of the year to the end of the year.

**Example 3:** Test Scores

In a math class, a student scored 80 out of 100 on the first test. On the second test, the student's score improved to 90 out of 100. What is the percent increase in the student's test score?

To find the percent increase, we can apply the same steps as we did for percent decrease.

Step 1: Identify the original value and the new value.

The original value is 80, and the new value is 90.

Step 2: Find the change in value.

Change = New value - Original value = 90 - 80 = 10.

Step 3: Calculate the percent increase.

Percent increase = (Change/Original value) × 100 = (10/80) × 100 = 12.5%.

Therefore, the student's test score increased by 12.5% from the first test to the second test.