Fractions and Decimals Quiz

Fractions and Decimals

Fractions

• Definition: A fraction represents a part of a whole and consists of a numerator (top) and a denominator (bottom).

• Types of Fractions:

  • Proper Fractions: Numerator is less than the denominator (e.g., 3/4).
  • Improper Fractions: Numerator is greater than or equal to the denominator (e.g., 5/3).
  • Mixed Numbers: A whole number combined with a proper fraction (e.g., 2 1/3).

• Equivalent Fractions: Different fractions that represent the same value (e.g., 1/2 = 2/4).

• Simplifying Fractions: Dividing both the numerator and denominator by their greatest common factor (GCF) to reduce the fraction (e.g., 4/8 simplifies to 1/2).

• Adding and Subtracting Fractions:

  • Same Denominator: Add or subtract numerators; keep the denominator (e.g., 1/4 + 2/4 = 3/4).
  • Different Denominators: Find a common denominator, convert fractions, then add or subtract.

• Multiplying Fractions: Multiply numerators together and denominators together (e.g., 1/2 × 3/4 = 3/8).

• Dividing Fractions: Multiply by the reciprocal of the divisor (e.g., 1/2 ÷ 3/4 = 1/2 × 4/3 = 2/3).

Decimals

• Definition: A decimal is a way to represent fractions using a base-10 system, shown with a decimal point (e.g., 0.75).

• Place Value:

  • Tenths (0.1), Hundredths (0.01), Thousandths (0.001), etc.
  • The position of digits to the right of the decimal indicates their value.

• Converting Fractions to Decimals:

  • Divide the numerator by the denominator (e.g., 1/4 = 0.25).
  • Recognize common fractions and their decimal equivalents (e.g., 1/2 = 0.5, 3/4 = 0.75).

• Converting Decimals to Fractions:

  • Write the decimal as a fraction with 1 in the denominator followed by as many zeros as there are digits after the decimal point, then simplify (e.g., 0.75 = 75/100 = 3/4).

• Adding and Subtracting Decimals:

  • Align decimal points and perform addition or subtraction (e.g., 2.5 + 3.75 = 6.25).

• Multiplying Decimals:

  • Multiply as whole numbers, then count total decimal places in both numbers to place the decimal in the product (e.g., 0.2 × 0.3 = 0.06).

• Dividing Decimals:

  • Move the decimal point of the divisor to make it a whole number, and do the same with the dividend; then divide normally (e.g., 0.6 ÷ 0.2 = 3).

Fractions

• A fraction consists of a numerator (top) and a denominator (bottom) representing a part of a whole.
• Proper Fractions: Numerator is less than the denominator (e.g., 3/4).
• Improper Fractions: Numerator is greater than or equal to the denominator (e.g., 5/3).
• Mixed Numbers: A combination of a whole number and a proper fraction (e.g., 2 1/3).
• Equivalent Fractions: Different fractions that express the same value (e.g., 1/2 equals 2/4).
• Simplifying Fractions: Reduce a fraction by dividing both the numerator and denominator by their greatest common factor (e.g., 4/8 simplifies to 1/2).
• Adding/Subtracting Fractions:
  • Same Denominator: Add or subtract numerators while keeping the same denominator (e.g., 1/4 + 2/4 equals 3/4).
  • Different Denominators: Find a common denominator before adding or subtracting fractions.
• Multiplying Fractions: Multiply numerators together and denominators together (e.g., 1/2 × 3/4 equals 3/8).
• Dividing Fractions: Divide by multiplying with the reciprocal of the divisor (e.g., 1/2 ÷ 3/4 equals 1/2 × 4/3 equals 2/3).

Decimals

• A decimal represents fractions using a base-10 system, illustrated with a decimal point (e.g., 0.75).
• Place Value: Decimal places are defined as tenths (0.1), hundredths (0.01), thousandths (0.001), etc.; the position indicates value.
• Converting Fractions to Decimals: Divide the numerator by the denominator (e.g., 1/4 converts to 0.25).
• Recognize common fractions and their decimal equivalents (e.g., 1/2 is 0.5, 3/4 is 0.75).
• Converting Decimals to Fractions: Express the decimal as a fraction (e.g., 0.75 equals 75/100), then simplify (e.g., 75/100 becomes 3/4).
• Adding/Subtracting Decimals: Align decimal points for addition or subtraction (e.g., 2.5 + 3.75 equals 6.25).
• Multiplying Decimals: Multiply as if they are whole numbers, then adjust the decimal in the product based on total decimal places (e.g., 0.2 × 0.3 equals 0.06).
• Dividing Decimals: Adjust the divisor to a whole number by moving the decimal, do the same with the dividend, and then divide as normal (e.g., 0.6 ÷ 0.2 results in 3).