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Questions and Answers
If 30% of a quantity is 45, what is the quantity?
If 30% of a quantity is 45, what is the quantity?
A shirt originally priced at $50 is on sale at 20% off. What is the sale price of the shirt?
A shirt originally priced at $50 is on sale at 20% off. What is the sale price of the shirt?
If the population of a city decreases by 15% from 800, what is the new population?
If the population of a city decreases by 15% from 800, what is the new population?
By what percent must a baker increase the price of a cake that costs $20 to make a profit of 25%?
By what percent must a baker increase the price of a cake that costs $20 to make a profit of 25%?
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If a student scored 80% on an exam and wants to increase their score to 90%, by what percent must they improve?
If a student scored 80% on an exam and wants to increase their score to 90%, by what percent must they improve?
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If the length of a rectangle increases by 10% and the width decreases by 5%, what is the net percentage change in the rectangle's area?
If the length of a rectangle increases by 10% and the width decreases by 5%, what is the net percentage change in the rectangle's area?
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If a store increases the price of a product by 40%, what is the new price if the original price was $80?
If a store increases the price of a product by 40%, what is the new price if the original price was $80?
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What would be the percentage increase if a shirt originally priced at $30 is marked up to $42?
What would be the percentage increase if a shirt originally priced at $30 is marked up to $42?
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If a product is discounted by 20% from its original price, what percentage increase from the discounted price is needed to get back to the original price?
If a product is discounted by 20% from its original price, what percentage increase from the discounted price is needed to get back to the original price?
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A computer originally priced at $1500 is on sale for $1200. What is the percentage discount being offered?
A computer originally priced at $1500 is on sale for $1200. What is the percentage discount being offered?
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If a company spends $600 on advertising and this represents 30% of their total budget, what is the company's total advertising budget?
If a company spends $600 on advertising and this represents 30% of their total budget, what is the company's total advertising budget?
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If a gadget's price is increased by 50% and then decreased by 40%, what is the overall percentage change in price?
If a gadget's price is increased by 50% and then decreased by 40%, what is the overall percentage change in price?
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Study Notes
Precise Percentages: Understanding and Applying Them
Percentages are a fundamental part of mathematical thinking and everyday life. They help us understand proportions, compare quantities, and make informed decisions. In this article, we'll delve into the world of percentages, exploring how they're used, and why they're essential in various scenarios.
What is a Percentage?
A percentage is simply a ratio of two quantities expressed as a fraction of 100. We use the symbol "%" to represent percentages. For example, if we have 60 apples out of a total of 100, we can say that 60 is 60% of 100.
Applications of Percentages
- Calculating Increases and Decreases
Percentages are commonly used to calculate increases or decreases in various quantities. For example,picture a store selling t-shirts for $10 each. They decide to increase the price by 25%. To find the new price, we multiply the original price by the percentage increase divided by 100. In this case, $10 * (1 + 0.25) = $12.50. Conversely, we can use percentages to calculate discounts, deducting the percentage discount from the original price.
- Converting Fractions to Percentages
If we have a fraction of a whole, we can convert it to a percentage by multiplying the fraction by 100. For example, ¾ can be written as 75%.
- Converting Percentages to Fractions
To convert a percentage to a fraction, we divide the percentage by 100. For example, 25% is equivalent to 25/100, which simplifies to 1/4.
- Finding Percentages of a Quantity
To find a percentage of a quantity, we multiply the quantity by the percentage converted to a decimal. For example, to find 20% of 40, we first convert 20% to a decimal (0.2). Then, we multiply 40 by 0.2 to get 8.
- Solving Percentage Problems
Percentage problems typically involve finding an unknown quantity based on information about a percentage of a given quantity. To solve these problems, we set up an equation with the given information and solve for the unknown in terms of the original quantity. For example, if we're told that 25% of a number is 15, we can set up the equation 0.25x = 15, where x represents the original quantity.
- Percentage Change
Percentage change helps us determine how much a quantity has increased or decreased relative to its original value. To find the percentage change, we first calculate the difference between the new and old values, then divide this difference by the original value and multiply by 100. For example, if the price of a laptop increased from $800 to $900, the percentage change is (900 - 800) / 800 * 100 = 12.5%, which means the price increased by 12.5%.
In the next section, we'll explore the idea of proportions, which is directly related to our understanding of percentages. Khan Academy. (n.d.). Percentages. Retrieved from https://www.khanacademy.org/math/arithmetic/fractions-decimals-percents/percentages Khan Academy. (n.d.). Percentage Problems. Retrieved from https://www.khanacademy.org/math/arithmetic/fractions-decimals-percents/percentage-problems/v/percentage-problems
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Description
Explore the concept of percentages, from basic definitions to practical applications like calculating increases, decreases, conversions between fractions and percentages, and solving percentage problems. Learn essential techniques for finding percentages of quantities and understanding percentage change.
