Mathematics
Grade 8
15 min
Compare percents of numbers
Compare percents of numbers
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Accurately calculate a percent of a given number.
Compare the numerical values of two different percents of different numbers.
Determine which of two or more 'percent of a number' expressions yields a greater or lesser value.
Solve real-world problems that require comparing percents of different quantities.
Explain why comparing percents directly without considering their base numbers can lead to incorrect conclusions.
Use inequality symbols (<, >, =) to represent comparisons between percents of numbers.
Ever wondered if '20% off a $100 shirt' is a better deal than '30% off an $80 shirt'? 🤔 Today, we'll learn how to figure out exactly which deal saves you more!
In this lesson, you'll learn how to calculate a...
2
Key Concepts & Vocabulary
TermDefinitionExample
PercentA ratio that compares a number to 100. It means 'per hundred' or 'out of 100'.25% means 25 out of 100, or the fraction 25/100.
Base NumberThe whole amount or total quantity from which a percentage is calculated. It's the 'of' number in a percent problem.In '20% of 50', the base number is 50.
Value of a PercentThe actual numerical amount that results from calculating a specific percentage of a given base number.The value of 20% of 50 is 10.
ComparisonThe act of examining two or more numbers or quantities to determine their relationship, such as which is greater, smaller, or if they are equal.Comparing 10 and 12, we find that 12 is greater than 10.
InequalityA mathematical statement that shows two values are not equal...
3
Core Formulas
Calculating a Percent of a Number
$$P\% \text{ of } N = \frac{P}{100} \times N$$
To find a percentage of any number, convert the percent to a decimal (by dividing by 100) or a fraction, and then multiply it by the base number. This rule helps you find the actual value represented by the percentage.
Comparing Two Numerical Values
$$A > B \quad \text{ (A is greater than B)}$$ $$A < B \quad \text{ (A is less than B)}$$ $$A = B \quad \text{ (A is equal to B)}$$
After calculating the actual values of the percents of numbers, use these inequality symbols to clearly state the comparison between the two resulting numbers. This is the final step in determining which value is greater, smaller, or if they are the same.
5 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
Given that A is 20% of B, and C is 50% of A. Which quantity is greater: 15% of B, or C? (Assume B is a positive number).
A.15% of B is greater.
B.is greater.
C.They are equal.
D.It depends on the value of B.
Challenging
A stock is priced at $100. On Monday, its price increases by 10%. On Tuesday, its price decreases by 10%. How does the final price on Tuesday compare to the original $100 price?
A.The final price is greater than $100.
B.The final price is equal to $100.
C.The final price is $99.90.
D.The final price is less than $100.
Challenging
Which of the following two values is greater? Value 1: 12.5% of 320. Value 2: (1/5) of 205.
A.Value 1 is greater.
B.Value 2 is greater.
C.The two values are equal.
D.The values are both integers.
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing Free