Finding the Part by Multiplying by the Percent Fraction
Finding the Part by Multiplying by the Percent Fraction is a Grade 6 math skill from Big Ideas Math, Course 1, Chapter 5: Ratios and Rates. To find a percent of a number: convert the percent to a fraction, then multiply by the whole. Formula: Part = (Percent/100) × Whole. Examples: 25% of 80 = (1/4) × 80 = 20; 60% of 50 = (3/5) × 50 = 30; 150% of 40 = (3/2) × 40 = 60. Simplifying the fraction before multiplying often makes the arithmetic easier.
Key Concepts
Property To find the percent of a number (the part), convert the percent to a fraction and multiply it by the whole number. $$ \text{Part} = \text{Percent (as a fraction)} \times \text{Whole} $$.
Examples What is $25\%$ of $80$? $$ \frac{25}{100} \times 80 = \frac{1}{4} \times 80 = 20 $$ Find $60\%$ of $50$. $$ \frac{60}{100} \times 50 = \frac{3}{5} \times 50 = 30 $$ What is $150\%$ of $40$? $$ \frac{150}{100} \times 40 = \frac{3}{2} \times 40 = 60 $$.
Explanation This method helps you calculate the "part" when you know the "percent" and the "whole". First, you must convert the percentage into its equivalent fraction by placing it over 100 and simplifying if possible. Then, multiply this fraction by the whole number to find the answer. This is a direct application of the concept that "of" in mathematics often means multiplication.
Common Questions
How do you find a percent of a number?
Convert the percent to a fraction by writing it over 100, simplify if possible, then multiply by the whole number. Example: 25% of 80 = 25/100 × 80 = 1/4 × 80 = 20.
What is the formula for finding the part?
Part = (Percent ÷ 100) × Whole. Equivalently, Part = Percent fraction × Whole. This formula works for any percent, including those over 100%.
What does 'of' mean in percent problems?
In math, 'of' usually means multiplication. '25% of 80' means 25/100 × 80. This is why finding a percent of a number involves multiplying the percent (as a fraction or decimal) by the whole number.
How do you find 150% of a number?
150% = 150/100 = 3/2. So 150% of 40 = 3/2 × 40 = 60. A percent over 100% gives an answer larger than the original number.
When do Grade 6 students learn to find percents of numbers?
This is covered in Big Ideas Math, Course 1, Chapter 5: Ratios and Rates, as part of Grade 6 work with ratios, proportions, and percents.
What is an easier way to find common percents?
Use fraction shortcuts: 50% = 1/2, 25% = 1/4, 75% = 3/4, 10% = 1/10, 20% = 1/5. For 10%, just move the decimal left one place. For other percents, convert to a simple fraction when possible.