Percents
63 flashcards covering Percents for the ACT Math section.
Percents are a way to express a portion of a whole as a fraction out of 100, making it easier to compare and calculate parts of quantities. For instance, if you have 25% of a pizza, that means you're dealing with a quarter of it. This concept is essential in math because it appears in everyday scenarios like discounts, tips, and growth rates, helping you understand relationships between numbers and solve practical problems.
On the ACT Math section, percents show up in questions that involve calculating percentages of numbers, percent change, or ratios in word problems, often mixed with other topics like algebra or geometry. Common traps include mistaking a percentage for a decimal or overlooking whether a problem asks for an increase or decrease, which can lead to careless errors. Focus on practicing conversions between fractions, decimals, and percents, as well as applying them to real-world contexts to build speed and accuracy.
Remember to practice with timed questions to improve your efficiency.
Terms (63)
- 01
Percent
A percent is a way to express a number as a fraction of 100, using the % symbol, commonly used in calculations involving parts of a whole.
- 02
Percentage
Percentage refers to the result of a percent calculation, such as 50% meaning 50 per 100 or 0.50.
- 03
Base in percentage problems
The base is the whole amount in a percentage problem, to which the rate is applied, such as the original price before a discount.
- 04
Rate of percent
The rate of percent is the percentage value itself, indicating how much of the base is being considered, like 20% in '20% of 100'.
- 05
Converting percent to decimal
To convert a percent to a decimal, divide the percent value by 100, such as turning 25% into 0.25 for easier calculations.
- 06
Converting decimal to percent
To convert a decimal to a percent, multiply the decimal by 100 and add the % symbol, like changing 0.75 to 75%.
- 07
Converting fraction to percent
To convert a fraction to a percent, divide the numerator by the denominator and multiply by 100, such as turning 1/4 into 25%.
- 08
Converting percent to fraction
To convert a percent to a fraction, write the percent over 100 and simplify, for example, changing 75% to 3/4.
- 09
Finding what percent one number is of another
To find what percent one number is of another, divide the first number by the second, multiply by 100, such as determining what percent 20 is of 50.
- 10
Percentage of a number formula
The formula to find a percentage of a number is (percentage / 100) multiplied by the number, used to calculate things like 10% of 200.
- 11
Percent increase
Percent increase measures how much a quantity has grown relative to its original value, calculated as the difference divided by the original, then multiplied by 100.
- 12
Percent decrease
Percent decrease measures how much a quantity has shrunk relative to its original value, calculated as the difference divided by the original, then multiplied by 100.
- 13
Percent increase formula
The formula for percent increase is [(new value - original value) / original value] × 100, used to find growth rates in various contexts.
- 14
Percent decrease formula
The formula for percent decrease is [(original value - new value) / original value] × 100, applied when values diminish over time.
- 15
Simple interest
Simple interest is the interest calculated only on the principal amount, not on accumulated interest, typically for a fixed period.
- 16
Simple interest formula
The simple interest formula is Interest = Principal × Rate × Time, where rate is annual and time is in years, used for loans or investments.
- 17
Principal in simple interest
The principal is the initial amount of money borrowed or invested in simple interest calculations, upon which interest is computed.
- 18
Rate in simple interest
The rate in simple interest is the annual percentage at which interest is calculated on the principal, expressed as a decimal or percent.
- 19
Time in simple interest
Time in simple interest refers to the duration for which the money is borrowed or invested, usually in years, affecting the total interest.
- 20
Compound interest
Compound interest is interest calculated on the initial principal and also on the accumulated interest of prior periods, leading to exponential growth.
- 21
Annual percentage rate (APR)
APR is the annual rate charged for borrowing or earning interest, expressed as a percentage, helping compare different financial options.
- 22
Discount percentage
Discount percentage is the percent reduction from the original price, calculated to find the sale price of an item.
- 23
Original price in discount
The original price is the full price before any discount is applied, serving as the base for percentage reduction calculations.
- 24
Sale price calculation
Sale price is calculated by subtracting the discount amount from the original price, where the discount is a percentage of the original.
- 25
Markup percentage
Markup percentage is the percent added to the cost price to determine the selling price, common in retail pricing strategies.
- 26
Cost price in markup
Cost price is the amount paid to acquire an item, which is then increased by a markup percentage to set the selling price.
- 27
Selling price in markup
Selling price is the final price at which an item is sold, calculated by adding the markup percentage to the cost price.
- 28
Sales tax calculation
Sales tax is a percentage added to the purchase price, calculated by multiplying the pre-tax amount by the tax rate.
- 29
Including tax in total cost
To find the total cost including tax, add the sales tax amount to the original price, ensuring all expenses are accounted for.
- 30
Commission calculation
Commission is a percentage of sales paid to a salesperson, calculated by multiplying the sales amount by the commission rate.
- 31
Gross commission
Gross commission is the total commission earned before any deductions, based on the percentage of sales achieved.
- 32
Profit percentage
Profit percentage is the percent of profit relative to the cost price, calculated as (profit / cost price) × 100.
- 33
Loss percentage
Loss percentage is the percent of loss relative to the cost price, calculated as (loss / cost price) × 100.
- 34
Mixture problems
Mixture problems involve combining substances with different concentrations to achieve a desired percentage, solved using weighted averages.
- 35
Concentration percentage
Concentration percentage expresses the amount of solute in a solution relative to the total solution, often as parts per hundred.
- 36
Dilution of solutions
Dilution involves adding solvent to a solution to decrease its concentration percentage, calculated based on initial and final volumes.
- 37
Ratios expressed as percentages
Ratios can be converted to percentages by dividing each part by the total and multiplying by 100, useful for comparing proportions.
- 38
Proportion with percentages
Proportions with percentages set up equations where percentages represent parts of a whole, solved by cross-multiplication.
- 39
Solving percent equations
Solving percent equations involves isolating the variable in equations that include percentages, often by converting to decimals first.
- 40
Cross-multiplication in percent proportions
Cross-multiplication is a method to solve proportions involving percentages, ensuring the equation balances correctly.
- 41
Percent of percent
A percent of percent is calculated by multiplying the two percentages after converting them to decimals, such as finding 10% of 20%.
- 42
Misreading percentage increases
A common error is misreading 'increased by X%' as 'X% of the new value' instead of the original, leading to incorrect calculations.
- 43
Percentage points vs. percent change
Percentage points measure absolute differences in percentages, while percent change measures relative differences, often confused in comparisons.
- 44
Successive percentage changes
Successive percentage changes are applied one after another, where the second is based on the result of the first, not the original value.
- 45
Reverse percentages
Reverse percentages involve finding the original amount before a percentage increase or decrease was applied, using algebraic equations.
- 46
Percentiles in data
A percentile indicates the value below which a given percentage of observations in a dataset fall, used in statistics and data analysis.
- 47
Interpreting percentages in graphs
Percentages in graphs represent proportions of the whole, requiring careful reading to understand data distributions accurately.
- 48
Probability as percentage
Probability can be expressed as a percentage by multiplying the probability fraction by 100, indicating the likelihood of an event.
- 49
Odds vs. percentage
Odds express the ratio of success to failure, while percentage expresses probability as a part per hundred, requiring conversion for comparison.
- 50
Weighted averages with percentages
Weighted averages incorporate percentages to reflect the importance of different values, calculated by multiplying each by its weight and dividing by total weight.
- 51
Example: 20% of 50
To find 20% of 50, multiply 50 by 0.20, resulting in 10, which illustrates basic percentage calculation.
For instance, 20% of 50 is 10.
- 52
Example: What is 25% of 200?
To find 25% of 200, multiply 200 by 0.25, yielding 50, demonstrating straightforward percentage application.
% of 200 equals 50.
- 53
Example: Increased by 15%
If a value is increased by 15%, multiply the original by 1.15, such as turning 100 into 115.
increased by 15% is 115.
- 54
Example: Discount of 10% on $100
A 10% discount on $100 means subtracting 10% of 100 (which is 10) from 100, resulting in a sale price of 90.
% off $100 is $90.
- 55
Example: Simple interest on $1000 at 5% for 2 years
Simple interest on $1000 at 5% for 2 years is calculated as $1000 × 0.05 × 2 = $100.
Interest earned is $100.
- 56
Example: Compound interest
For $1000 at 5% compounded annually for 2 years, the amount is $1000 × (1 + 0.05)^2 = $1102.50.
Final amount is $1102.50.
- 57
Strategy for word problems
In percentage word problems, identify the base, rate, and part, then use the appropriate formula to set up and solve the equation.
- 58
Checking calculations in percentages
To check percentage calculations, verify by reversing the operation or using alternative methods, ensuring accuracy in results.
- 59
Avoiding decimal errors in percentages
When working with percentages, always convert to decimals correctly by dividing by 100 to prevent errors in multiplication or addition.
- 60
Understanding successive discounts
Successive discounts are applied one after another on the reduced price, not the original, affecting the final price cumulatively.
- 61
Percent in ratios
Percentages can represent ratios by expressing the ratio as a fraction and converting to a percentage of the total.
- 62
Fractional percentages
Fractional percentages, like 12.5%, are decimals expressed as percentages, calculated by multiplying the fraction by 100.
- 63
Percentage error
Percentage error measures the accuracy of a measurement by comparing the difference from the true value to the true value, then multiplying by 100.