Glossary
"Is over Of" Trick
A mnemonic for solving percentage problems: (Part / Whole) = (Percent / 100), often phrased as 'Is/Of = %/100'. It helps set up proportions to find an unknown value.
Example:
If 20 is what percent of 80, you'd set up 20/80 = x/100 to find x, which is 25. This trick can quickly solve many percentage word problems.
Decimal to Fraction Conversion
To convert a decimal to a fraction, write the decimal as a fraction over a power of 10 (e.g., 0.25 = 25/100) and then simplify the fraction.
Example:
Converting 0.6 to a fraction means writing it as 6/10, which simplifies to 3/5. This is useful for problems requiring answers in simplest form.
Decimal to Percentage Conversion
To convert a decimal to a percentage, multiply the decimal by 100 and add the percent (%) symbol.
Example:
To express 0.75 as a percentage, you multiply 0.75 by 100, resulting in 75%. This is often used when reporting test scores.
Finding New Value Directly (Percent Change)
To find a new value after a percent change, multiply the original value by (1 + percentage as a decimal) for an increase, or (1 - percentage as a decimal) for a decrease.
Example:
If a 75 * (1 - 0.20) = $60. This method is a time-saver on the SAT.
Finding a Percentage of a Quantity
To calculate a percentage of a given quantity, convert the percentage to a decimal and then multiply it by the quantity.
Example:
To find 15% of 200, you'd calculate 0.15 * 200, which equals 30. This skill is vital for solving discount problems.
Fraction to Decimal Conversion
To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number).
Example:
Converting 3/8 to a decimal involves dividing 3 by 8, which yields 0.375. This is a fundamental skill for comparing different number forms.
Fraction to Percentage Conversion
To convert a fraction to a percentage, first convert the fraction to a decimal, then multiply the decimal by 100 and add the percent (%) symbol.
Example:
To express 1/4 as a percentage, first convert it to 0.25, then multiply by 100 to get 25%. This helps in understanding proportions visually.
Percent Decrease
The relative reduction in a quantity, calculated as ((Original Value - New Value) / Original Value) * 100. It indicates how much a value has shrunk from its initial state.
Example:
If a car's value drops from 18,000, the percent decrease is ((18,000) / $20,000) * 100 = 10%. This is common in depreciation calculations.
Percent Increase
The relative increase in a quantity, calculated as ((New Value - Original Value) / Original Value) * 100. It shows how much a value has grown compared to its starting point.
Example:
If a stock price goes from 60, the percent increase is ((50) / $50) * 100 = 20%. Understanding this helps analyze market trends.
Percentage
A number or ratio expressed as a fraction of 100, denoted by the percent sign (%). It represents a part of a whole, where the whole is considered 100%.
Example:
If you score 90 out of 100 on a test, your score is 90%, meaning 90 parts out of every 100. This is a great score to aim for on the SAT!
Percentage to Decimal Conversion
To convert a percentage to a decimal, divide the percentage by 100 (or move the decimal point two places to the left).
Example:
To use 45% in a calculation, convert it to 0.45. This step is crucial for applying percentages in formulas.
Successive Percent Changes
When multiple percentage changes are applied sequentially, they cannot be simply added or subtracted. Each change must be applied to the *new* resulting value.
Example:
If a price increases by 10% and then decreases by 10%, the final price is not the original price. You must multiply the original price by (1 + 0.10) and then by (1 - 0.10) to find the true net change.