Solving for the Unknown: Finding the Part
Solving for the Unknown: Finding the Part is a Grade 7 math skill in Reveal Math Accelerated, Unit 3: Solve Problems Involving Percentages, where students use the percent equation Part = Percent x Whole to solve for the part when the percent and whole are given. This is one of the three basic percent problem types and is essential for calculating taxes, tips, discounts, and other real-world applications.
Key Concepts
Property To find the part of a whole in a real world context, use the percent equation: $$\text{part} = \text{percent} \times \text{whole}$$ Remember to convert the percent to a decimal (by dividing by $100$) before multiplying.
Examples Tip: A meal costs $40$ dollars. If you want to leave a $15\%$ tip, what is the amount of the tip? Convert $15\%$ to $0.15$, then multiply: $\text{part} = 0.15 \times 40 = 6$ dollars. Discount: A jacket is originally priced at $80$ dollars and is on sale for $25\%$ off. What is the discount amount? Convert $25\%$ to $0.25$, then multiply: $\text{part} = 0.25 \times 80 = 20$ dollars. Commission: A salesperson earns a $5\%$ commission on a car sold for $20,000$ dollars. How much is the commission? Convert $5\%$ to $0.05$, then multiply: $\text{part} = 0.05 \times 20000 = 1000$ dollars.
Explanation To find the "part" in a real world scenario like calculating a tip, tax, or discount, you can use the percent equation directly. First, always convert the given percent into a decimal by dividing it by $100$. Then, multiply this decimal by the "whole" amount (such as the original price or total bill) to find the specific part you are looking for. This straightforward multiplication helps you quickly determine extra costs, earnings, or savings in everyday situations.
Common Questions
How do you find the part in a percent problem?
Use the formula: Part = Percent x Whole. Convert the percent to a decimal or fraction, then multiply by the whole. For example, 30% of 80 = 0.30 x 80 = 24.
What are the three types of percent problems?
The three types are: (1) find the part (Part = Percent x Whole), (2) find the percent (Percent = Part / Whole), and (3) find the whole (Whole = Part / Percent).
What real-world situations use finding the part?
Calculating a 15% tip on a restaurant bill, finding the sale discount on a price, computing sales tax, or determining a commission all require finding the part of a whole.
What is Reveal Math Accelerated Unit 3 about?
Unit 3 covers Solve Problems Involving Percentages, including percent equations, percent change, percent error, markup, discount, and simple interest.