Finding what percent a part is
Finding what percent a part is of a whole is a key percent skill in Grade 8 math (Yoshiwara Core Math). The formula: percent = (part ÷ whole) × 100. For example, 15 out of 60 students = (15/60) × 100 = 25%. This reverses the process of finding a percent of a number. It is essential for test scores, discounts, statistics, and any context requiring a proportional comparison. The three-part relationship (percent, part, whole) enables solving any combination when two values are known.
Key Concepts
Property To find what percent a part is of a whole: 1. Divide the part by the whole to get a decimal fraction: $$\frac{\text{part}}{\text{whole}}$$ 2. Multiply the decimal fraction by 100 to convert it to a percent.
Examples You scored 18 points out of a total of 20 on a quiz. To find your percent score, divide the part by the whole: $18 \div 20 = 0.90$. Multiply by 100 to get the percent: $0.90 \times 100 = 90\%$. A recipe calls for 400 grams of flour, and you have used 80 grams. The percent used is $80 \div 400 = 0.20$. This is equivalent to $20\%$. If you saved 30 dollars on an item that originally cost 150 dollars, you saved $\frac{30}{150} = 0.2$. As a percent, this is $0.2 \times 100 = 20\%$.
Explanation This process reverses the calculation. By dividing the smaller part by the total whole, you find the fraction it represents. Multiplying by 100 scales that fraction up to a percentage, making it easier to understand.
Common Questions
What is the formula for finding what percent a part is?
Percent = (part ÷ whole) × 100. For example, 15 out of 60 = (15/60) × 100 = 25%.
How do you find what percent 18 is of 72?
18/72 × 100 = 0.25 × 100 = 25%.
How is this different from finding a percent of a number?
Finding 25% of 60 gives 15 (part). Finding what percent 15 is of 60 gives 25% (percent). Opposite direction.
What are the three quantities in any percent problem?
Percent (%), part (portion), and whole (base). Knowing two lets you find the third.
How do you check your answer?
Apply the percent back: 25% of 60 = 15, confirming 15 is 25% of 60. ✓