To find the percent of 25, we first need to understand what a percent is. A percent is a ratio that compares a number to 100. For example, 25% means 25 out of 100. So to find the percent of 25, we need to set up a ratio where the part is 25 and the whole is 100.
Setting Up the Ratio
To find the percent, we use the following ratio:
Part/Whole = Percent/100
Let’s plug in the numbers we know:
25/100 = Percent/100
25 is the part and 100 is the whole. We want to solve for the percent.
Solving the Equation
To solve this equation, we simplify the right side:
25/100 = Percent/100
25/100 = Percent/100
(25/100) * (100/1) = (Percent/100) * (100/1)
25/1 = Percent/1
Percent = 25
Therefore, the percent of 25 is 25%.
Explaining the Answer
The reason the percent of 25 is 25% is because the number 25 makes up 25 out of 100 parts. 25% means 25 parts out of a total of 100 parts. So 25 is 25% of 100.
This makes sense if we think about percentages as fractions:
25/100 can be reduced to 1/4
1/4 = 25%
So 25 is 25% of 100.
Checking the Answer
We can double check our work by taking the percent and converting it back to the original numbers:
25% of 100
0.25 * 100 = 25
Therefore, if 25% of 100 is 25, then the percent of 25 must be 25%.
Examples
Let’s look at some more examples to drive home the concept:
Example 1
What is the percent of 50?
Using the same steps:
Part/Whole = Percent/100
50/100 = Percent/100
Percent = 50
The percent of 50 is 50%.
Example 2
What is the percent of 10?
Part/Whole = Percent/100
10/100 = Percent/100
Percent = 10
The percent of 10 is 10%.
Example 3
What is the percent of 75?
75/100 = Percent/100
Percent = 75
The percent of 75 is 75%.
Common Percentages
Here is a table of some common percentages and their decimal and fraction equivalents:
| Percent | Decimal | Fraction |
|---|---|---|
| 25% | 0.25 | 1/4 |
| 50% | 0.5 | 1/2 |
| 75% | 0.75 | 3/4 |
| 100% | 1 | 1/1 |
This table gives you a sense of what some common percentages look like as decimals and fractions.
Applications of Percents
Knowing how to find a percent is useful for:
– Calculating tips, commissions, and discounts
– Creating mixtures and solutions
– Comparing parts to wholes (e.g. what percentage of students passed an exam)
– Expressing probability as a ratio of favorable to total outcomes
– Converting between percents, decimals, and fractions
Let’s look at some examples:
Tip Calculation
If a meal costs $25 and you want to tip 20%, you would calculate:
20% of $25 = 0.20 * $25 = $5 tip
So 20% of $25 is $5.
Mixture Problem
If you want to make a 30% saline solution, you would mix:
30 parts saline (the solute)
70 parts water (the solvent)
The 30% represents the ratio of saline to the total solution.
Exam Performance
If 15 out of 20 students passed an exam, the percent who passed is:
Part who passed / Whole class = 15/20 = 75%
So 75% of the class passed the exam.
Converting Percents
You can convert between percents, decimals, and fractions:
25% = 0.25 = 1/4
50% = 0.5 = 1/2
75% = 0.75 = 3/4
To convert a decimal to a percent, multiply by 100:
0.35 * 100 = 35%
To convert a fraction, divide the numerator by the denominator:
3/5 = 3/5 * 100% = 60%
Practice converting between these formats.
Finding the Whole
Sometimes you know the percent and the part, but need to find the whole.
For example, if 30% of a number is 18, what is the whole number?
Let’s set up an equation:
Part/Whole = Percent/100
18/Whole = 30/100
(18 * 100)/Whole = (30 * 1)
1800/Whole = 30
Whole = 1800/30
Whole = 60
So 30% of the whole is 18, and the whole is 60.
Word Problems
Let’s practice some word problems involving percents:
Word Problem 1
A hat is normally $50, but goes on sale for 20% off. What is the sale price of the hat?
To find the sale price, we calculate 20% of $50:
20% of $50 is 0.2 * $50 = $10
So the hat is discounted by $10.
The original price was $50.
So the sale price is $50 – $10 = $40.
Therefore, the sale price of the hat is $40.
Word Problem 2
A bookstore orders 200 copies of a book. The books cost the bookstore $20 each wholesale. The bookstore wants to sell the books at a 45% markup over wholesale. What will the bookstore charge for each book?
The wholesaler price per book is $20.
The markup percentage is 45%.
To calculate the markup amount:
45% of $20 is 0.45 * $20 = $9
So the markup is $9 per book.
The bookstore paid $20 wholesale per book.
The markup is $9 per book.
So the retail price will be:
$20 + $9 = $29
Therefore, with a 45% markup the bookstore will charge $29 per book.
Word Problem 3
A salesperson earns an 8% commission on their total sales. Last month they sold $50,000 worth of product. How much commission did they earn?
The sales amount is $50,000.
The commission rate is 8%.
To calculate the commission:
8% of $50,000 is 0.08 * $50,000 = $4,000
Therefore, with 8% commission on $50,000 of sales, the salesperson earned $4,000 in commission.
Conclusion
In summary, to find the percent of a number:
– Set up a ratio between the part and whole, with the whole being 100
– The resulting ratio is the percent
– 25 is 25% of 100 because 25/100 reduces to 1/4, or 25%
Percents are useful for calculations like discounts, mixtures, comparisons and conversions. Make sure you understand how to:
– Find a percentage of a number
– Convert between percents, decimals and fractions
– Solve word problems using percentages
With practice, finding percents will become second nature. Understanding percents unlocks your ability to calculate discounts, compare values, express probabilities, and more. It is an essential math and analytical skill.