Understanding Fractions

Fractions

• A fraction represents a part of a whole
• Consists of a numerator (top number) and a denominator (bottom number)
• Examples:
  • 1/2 (one half)
  • 3/4 (three quarters)
• Equivalent fractions:
  • Fractions with the same value, but different numbers
  • Example: 1/2 = 2/4 = 3/6
• Comparing fractions:
  • Compare the numerators (top numbers) if the denominators (bottom numbers) are the same
  • Compare the denominators (bottom numbers) if the numerators (top numbers) are the same

Decimals

• A decimal is a way to represent a fraction using a point and digits
• Examples:
  • 0.5 (one half)
  • 0.75 (three quarters)
• Converting fractions to decimals:
  • Divide the numerator by the denominator
  • Example: 3/4 = 3 ÷ 4 = 0.75
• Comparing decimals:
  • Compare the digits from left to right
  • Compare the number of digits after the point

Basic Geometry

• Points, Lines, and Planes:
  • A point has no size, only location
  • A line extends infinitely in two directions
  • A plane is a flat surface that extends infinitely
• Basic Shapes:
  • Square: 4 right angles, 4 sides of equal length
  • Rectangle: 4 right angles, opposite sides of equal length
  • Triangle: 3 sides, 3 angles
• Measuring Angles:
  • Right angle: 90 degrees
  • Acute angle: less than 90 degrees
  • Obtuse angle: more than 90 degrees

Fractions

• A fraction is a way to represent a part of a whole
• Consists of a numerator (top number) and a denominator (bottom number)
• Examples: 1/2 (one half), 3/4 (three quarters)
• Equivalent fractions have the same value, but different numbers
• Example: 1/2 = 2/4 = 3/6

Comparing Fractions

• Compare numerators (top numbers) if denominators (bottom numbers) are the same
• Compare denominators (bottom numbers) if numerators (top numbers) are the same

Decimals

• A decimal is a way to represent a fraction using a point and digits
• Examples: 0.5 (one half), 0.75 (three quarters)
• To convert a fraction to a decimal, divide the numerator by the denominator
• Example: 3/4 = 3 ÷ 4 = 0.75

Comparing Decimals

• Compare digits from left to right
• Compare the number of digits after the point

Basic Geometry

Points, Lines, and Planes

• A point has no size, only location
• A line extends infinitely in two directions
• A plane is a flat surface that extends infinitely

Basic Shapes

• Square: 4 right angles, 4 sides of equal length
• Rectangle: 4 right angles, opposite sides of equal length
• Triangle: 3 sides, 3 angles

Measuring Angles

• Right angle: 90 degrees
• Acute angle: less than 90 degrees
• Obtuse angle: more than 90 degrees

Fractions

• A fraction represents part of a whole, consisting of a numerator (top number) and a denominator (bottom number)
• Numerator indicates how many equal parts we have, while the denominator indicates how many parts the whole is divided into
• Types of fractions include:
  • Proper fractions: numerator is less than the denominator (e.g. 1/2)
  • Improper fractions: numerator is greater than or equal to the denominator (e.g. 3/2)
  • Mixed numbers: a combination of a whole number and a proper fraction (e.g. 2 1/2)
• Equivalent fractions have the same value and can be created by multiplying or dividing both the numerator and denominator by the same number
• Compare fractions by comparing numerators if denominators are the same, or by comparing denominators if numerators are the same
• Use equivalent fractions to compare fractions with different denominators

Decimals

• A decimal represents part of a whole using a point and digits
• Decimal point separates the whole part from the fractional part
• Decimals can be used to represent fractions and mixed numbers
• Read decimals as "and" (e.g. 3.5 is read as "three and five tenths")
• Write decimals with the correct number of digits after the decimal point
• Compare decimals by comparing digits after the decimal point, following the same rules as comparing whole numbers (e.g. 3.5 is greater than 3.4)
• Convert a fraction to a decimal by dividing the numerator by the denominator
• Convert a decimal to a fraction by finding the equivalent fraction (e.g. 0.5 is equivalent to 1/2)