Questions and Answers
How do you calculate 25% of a number?
Which of the following expresses a part-to-whole ratio?
If you convert 5 miles to kilometers, what is the correct value?
What is the greatest common divisor (GCD) of 12 and 18?
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Which method is appropriate for converting a measurement using a conversion factor?
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Study Notes
Percentages
- Definition: A percentage is a fraction expressed as a part of 100.
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Calculation:
- To find a percentage of a number: (Percentage/100) × Total.
- To convert a fraction to a percentage: (Numerator/Denominator) × 100%.
- To convert a decimal to a percentage: Multiply by 100.
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Applications:
- Used in finance for interest rates, discounts, and tax calculations.
- Common in statistics for data representation.
Ratios
- Definition: A ratio is a comparison of two quantities, showing the relative sizes of two or more values.
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Formats:
- Can be expressed in three ways: a:b, a/b, or as a fraction.
- Simplification: Ratios can be simplified by dividing both sides by their greatest common divisor (GCD).
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Types:
- Part-to-part (e.g., ratio of boys to girls).
- Part-to-whole (e.g., ratio of boys to total students).
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Applications:
- Used in recipes, mixtures, and comparing quantities in various fields.
Unit Conversion
- Definition: The process of converting a quantity from one unit to another.
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Common Conversions:
- Length: 1 inch = 2.54 cm; 1 mile = 1.60934 km.
- Weight: 1 pound = 0.453592 kg; 1 ounce = 28.3495 grams.
- Volume: 1 gallon = 3.78541 liters; 1 liter = 33.814 ounces.
- Conversion Factors: A conversion factor is a ratio that expresses how many of one unit are equal to another unit.
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Method:
- Multiply the quantity by the appropriate conversion factor to obtain the desired unit.
- Applications: Essential in science, engineering, and daily life for accurate measurements.
Percentages
- A percentage represents a fraction denoting parts per hundred.
- To calculate the percentage of a number: multiply the number by the percentage and divide by 100.
- Converting fractions to percentages requires dividing the numerator by the denominator and multiplying by 100%.
- To convert decimals into percentages, simply multiply by 100.
- Percentages are commonly utilized in finance for calculating interest, discounts, and taxes.
- In statistics, percentages are vital for representing data visually and analytically.
Ratios
- A ratio compares two or more quantities, highlighting their relative sizes.
- Ratios can be displayed in three formats: a:b, a/b, or as a fraction.
- Simplification of ratios involves dividing both components by their greatest common divisor (GCD).
- Types of ratios include part-to-part (e.g., boys to girls) and part-to-whole (e.g., boys to total students).
- Ratios find application in recipes, mixtures, and in various fields for quantity comparison.
Unit Conversion
- Unit conversion is the transformation of a measurement from one unit to another.
- Common length conversions include: 1 inch equals 2.54 cm and 1 mile equals 1.60934 km.
- For weight, 1 pound is equivalent to 0.453592 kg and 1 ounce equals 28.3495 grams.
- In volume, 1 gallon is approximately 3.78541 liters, while 1 liter is around 33.814 ounces.
- A conversion factor is a ratio that defines how many units of one measure equate to another.
- To convert quantities, multiply by the appropriate conversion factor to switch between units.
- Unit conversion is crucial in science, engineering, and daily activities for precise measurements.
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Description
Test your understanding of percentages and ratios with this engaging quiz. Learn the definitions, calculations, and applications of these important mathematical concepts. Perfect for students looking to enhance their knowledge in mathematics!
