Find the total given a part and a percent

Learning Objectives Define 'part,' 'percent,' and 'total' in the context of percentage problems. Convert percentages to decimals for calculation purposes. Set up and solve a proportion to find the total when given a part and a percent. Use the percentage equation (Part = Percent × Total) to solve for the total. Solve real-world problems involving finding the total amount. Check the reasonableness of their calculated total. Ever wonder how stores calculate the original price of an item when it's on sale, and you only know the discount amount? 🛍️ In this lesson, you'll learn how to work backward from a known part and its corresponding percentage to discover the entire, original amount, also known as the total. This skill is crucial for...

TermDefinitionExample PartThe specific amount or quantity that represents a portion or piece of the total.If 20 students represent 10% of the school's population, then 20 is the 'part'. PercentA ratio that compares a number to 100, meaning 'per one hundred'. It indicates how many parts out of 100.10% means 10 out of every 100, or $\frac{10}{100}$. Total (Whole)The entire amount, the full quantity, or the original number from which a part is taken.The total number of students in the entire school is the 'total'. Decimal EquivalentA percentage expressed as a decimal by dividing the percent value by 100.To convert 25% to a decimal, you divide 25 by 100, which equals 0.25. ProportionAn equation that states that two ratios are equal. It's often used to s...

Percent Proportion $\frac{\text{Part}}{\text{Total}} = \frac{\text{Percent}}{100}$ This proportion can be used to find any of the three values (part, total, or percent) when the other two are known. For finding the total, you'll set up the proportion and then cross-multiply to solve for the unknown total. Percent Equation (Solving for Total) $\text{Total} = \frac{\text{Part}}{\text{Percent (as a decimal)}}$ This rule is derived from the basic percent equation (Part = Percent × Total). To use it, first convert the given percent into its decimal equivalent, then divide the 'part' by this decimal to find the 'total'.