The Percent Equation
The Percent Equation presents the formula Part = Percent × Whole to solve all three types of percent problems: finding the part, finding the percent, or finding the whole. Covered in Illustrative Mathematics Grade 6, Unit 6: Expressions and Equations, Grade 6 students represent the unknown with a variable and solve using division. This algebraic approach to percent problems replaces rote methods with a flexible equation that handles any percent question.
Key Concepts
Property To solve percentage problems, you can use the equation: $$ \text{Part} = \text{Percent} \times \text{Whole} $$ The percent must be written as a decimal or a fraction. You can represent the unknown value with a variable.
Examples What is $20\%$ of $50$? Let $x$ be the unknown part. $x = 0.20 \times 50$ $x = 10$ $12$ is what percent of $60$? Let $p$ be the unknown percent. $12 = p \times 60$ $p = \frac{12}{60} = 0.20$, which is $20\%$. $15$ is $30\%$ of what number? Let $w$ be the unknown whole. $15 = 0.30 \times w$ $w = \frac{15}{0.30} = 50$.
Explanation This skill applies your ability to write algebraic expressions to real world percentage scenarios. By translating the words "is," "of," and "what" into mathematical symbols ($=$, $\times$, variable), you can create a solvable equation. Remember to convert the percentage to its decimal form for calculation by dividing by 100. This method allows you to find any missing part of a percentage problem: the part, the whole, or the percent itself.
Common Questions
What is the percent equation?
The percent equation is: Part = Percent × Whole. Write the percent as a decimal, then solve for the unknown quantity.
How do you find what percent one number is of another?
Divide the part by the whole: Percent = Part ÷ Whole. Then convert the decimal to a percentage by multiplying by 100.
How do you find the whole when you know the part and percent?
Rearrange the equation: Whole = Part ÷ Percent. Convert the percent to a decimal first.
Where is the percent equation in Illustrative Mathematics Grade 6?
The percent equation is covered in Unit 6: Expressions and Equations of Illustrative Mathematics Grade 6.
How do you use the percent equation to find 30% of 80?
Part = 0.30 × 80 = 24. Write the percent as a decimal (30% = 0.30) before multiplying.