Fractions, Decimals, and Percentages

1. Fractions

• Definition: A fraction represents a part of a whole.

• Structure:

  • Numerator: The top number, indicating how many parts are being considered.

  • Denominator: The bottom number, indicating the total number of equal parts in the whole.

• Types:

  • Proper Fraction: Numerator is smaller than the denominator (e.g., 1/2, 3/4).

  • Improper Fraction: Numerator is greater than or equal to the denominator (e.g., 5/4, 7/7).

  • Mixed Number: A whole number and a proper fraction combined (e.g., 1 1/2).

• Operations:

  • Addition/Subtraction: Requires common denominators.

  • Multiplication: Multiply numerators together and denominators together.

  • Division: Invert the divisor (second fraction) and multiply.

2. Decimals

• Definition: A number that uses a decimal point to separate the whole number part from the fractional part.

• Place Value: Each digit after the decimal point represents a decreasing power of 10 (tenths, hundredths, thousandths, etc.).

• Operations: Performed similarly to whole numbers, with careful alignment of the decimal point.

3. Percentages

• Definition: A way to express a number as a fraction of 100.

• Symbol: % (percent)

• Conversion:

  • Fraction to Percentage: Multiply the fraction by 100%.

  • Decimal to Percentage: Multiply the decimal by 100%.

  • Percentage to Decimal: Divide the percentage by 100.

  • Percentage to Fraction: Write the percentage as a fraction with 100 as the denominator and simplify.

Key Concepts

• Equivalence: Fractions, decimals, and percentages can represent the same value.

• Conversions: You can easily convert between these forms.

• Real-World Applications: These concepts are used extensively in everyday life (e.g., sales, discounts, interest rates, cooking).

Example

Let's consider the fraction 1/4:

• Decimal: 1/4 = 0.25

• Percentage: 0.25 * 100% = 25%

This demonstrates that 1/4, 0.25, and 25% all represent the same portion of a whole.