Understanding Fractions

Study Notes

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

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

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

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

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)