Lesson 6: Finding Percent of Change

New Concept

The percent of change is the increase or decrease given as a percent of the original amount.

What’s next

Next, you'll apply this formula to calculate increases and decreases and solve real-world problems involving discounts and markups.

From 150 to 180 is an increase. Percent change = $\frac{180 - 150}{150} = \frac{30}{150} = 0.2 = 20\%$ increase. From 20 to 17 is a decrease. Percent change = $\frac{20 - 17}{20} = \frac{3}{20} = 0.15 = 15\%$ decrease.

Think of this as a "change score" for numbers. We measure how much a value has grown or shrunk compared to where it started. It is like checking your video game score's jump from one level to the next, but we turn that fraction into a percentage to make it super easy to compare big changes!

To write a decimal as a percent, multiply the decimal by 100. To write a fraction as a percent, first convert it to a decimal by dividing the numerator by the denominator, then multiply by 100.

To convert $0.045$ to a percent: $0.045 \times 100 = 4.5\%$. To convert $\frac{3}{8}$ to a percent: $3 \div 8 = 0.375$, so $0.375 \times 100 = 37.5\%$. To convert $5$ to a percent: $5 \times 100 = 500\%$.

Turning a number into a percent is like giving it a "per 100" makeover. "Percent" literally means "per hundred," so we just multiply by 100 to see how many parts out of a hundred it represents. For fractions, we just do the division first to get a decimal, then it is a simple hop to percent-land!

A 120 dollars jacket is on sale for 25% off. Discount = $0.25 \times 120 = 30$ dollars. Sale price = $120 - 30 = 90$ dollars. Find the sale price of a 50 dollars game with a 10% discount: $s = 50 - (0.10 \times 50) = 50 - 5 = 45$ dollars.

Ever seen a "20% off" sign? That is a discount! To find the final price, you first figure out the discount amount (the percentage of the original price) and then subtract it from the original tag. It’s like the store is giving you a cash rebate right at the register, so you pay less. Cha-ching!