Understanding percentages is an essential math skill used in everyday life. From calculating discounts while shopping to determining interest rates, percentages help us compare numbers efficiently. This lesson focuses on reteaching how to find the percent of a number using simple methods and examples.
What is a Percent?
A percent is a way to express a number as a fraction of 100. The symbol for percent is %, which means ‘per hundred.’ For example:
- 50% means 50 out of 100 or 50/100 (which simplifies to 1/2).
- 25% means 25 out of 100 or 25/100 (which simplifies to 1/4).
- 75% means 75 out of 100 or 75/100 (which simplifies to 3/4).
Understanding this concept is the foundation for calculating the percent of a number.
How to Find the Percent of a Number
There are three main methods to calculate the percent of a number:
- Using Multiplication
- Using Proportions
- Using Decimals
Each method provides the same result, so you can choose the one that feels easiest to use.
Method 1: Using Multiplication
To find the percent of a number using multiplication, follow these steps:
- Convert the percent into a fraction or decimal.
- Multiply the fraction or decimal by the given number.
Example 1: Finding 20% of 50
-
Convert 20% to a fraction:
20% = frac{20}{100} = 0.2 -
Multiply by 50:
0.2 times 50 = 10
Answer: 20% of 50 is 10.
Example 2: Finding 15% of 80
-
Convert 15% to a decimal:
15% = frac{15}{100} = 0.15 -
Multiply by 80:
0.15 times 80 = 12
Answer: 15% of 80 is 12.
Method 2: Using Proportions
A proportion is an equation that shows two ratios are equal. To use this method:
- Set up a proportion where percent/100 equals part/whole.
- Solve for the missing number.
Example: Finding 30% of 90
-
Set up the proportion:
frac{30}{100} = frac{x}{90} -
Solve for x by cross multiplying:
30 times 90 = 100 times x2700 = 100xx = frac{2700}{100} = 27
Answer: 30% of 90 is 27.
Method 3: Using Decimals
Another simple way to find the percent of a number is by converting the percentage into a decimal and then multiplying.
Example: Finding 25% of 200
-
Convert 25% to a decimal:
25% = 0.25 -
Multiply:
0.25 times 200 = 50
Answer: 25% of 200 is 50.
Example: Finding 8% of 150
-
Convert 8% to a decimal:
8% = 0.08 -
Multiply:
0.08 times 150 = 12
Answer: 8% of 150 is 12.
Common Applications of Percentages
1. Finding Discounts in Shopping
Stores often offer discounts as percentages. To calculate the discount amount:
- Multiply the original price by the discount percentage (converted into a decimal).
- Subtract the discount from the original price.
Example: A $100 item is on sale for 30% off
-
Convert 30% to a decimal: 0.30
-
Multiply by the price:
0.30 times 100 = 30 -
Subtract from the original price:
100 – 30 = 70
The sale price is $70.
2. Calculating Tips at a Restaurant
Tipping is common in restaurants, usually 15% or 20% of the total bill.
Example: A $50 bill with a 20% tip
- Convert 20% to a decimal: 0.20
- Multiply by 50:
0.20 times 50 = 10
The tip is $10, making the total bill $60.
3. Determining Tax on a Purchase
Sales tax is a percentage added to the purchase price.
Example: A $120 purchase with a 5% sales tax
-
Convert 5% to a decimal: 0.05
-
Multiply by 120:
0.05 times 120 = 6 -
Add the tax to the original price:
120 + 6 = 126
The total cost is $126.
4. Finding Test Scores and Grades
Grades are often given as percentages.
Example: A student scores 45 out of 50 on a test. What is the percentage?
-
Set up the proportion:
frac{x}{100} = frac{45}{50} -
Cross multiply:
50x = 4500 -
Solve for x :
x = 90
The student scored 90%.
Key Takeaways
? Percent means ‘per hundred’.
? To find the percent of a number, multiply the percentage (as a decimal) by the number.
? You can also use proportions to solve percent problems.
? Knowing how to calculate percentages is useful for shopping, tipping, taxes, and grades.
By practicing these methods, you can confidently work with percentages in real-life situations!
