Types of Fractions and Equivalent Fractions

Types of Fractions

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

Equivalent Fractions

• Equivalent Fractions: fractions that have the same value but different forms (e.g. 1/2 = 2/4 = 3/6)
• Can be obtained by multiplying or dividing both numerator and denominator by the same number

Simplifying Fractions

• Simplifying Fractions: reducing a fraction to its simplest form by dividing both numerator and denominator by their greatest common divisor (GCD)
• Example: 6/8 = 3/4 (divided by GCD of 6 and 8, which is 2)

Comparing Fractions

• Comparing Fractions: determining which fraction is larger or smaller
• Can be done by converting fractions to equivalent fractions with the same denominator, or by comparing the numerators and denominators separately

Operations with Fractions

• Addition and Subtraction: require common denominators
  • Example: 1/4 + 1/4 = 2/4
  • Example: 2/3 - 1/3 = 1/3
• Multiplication: multiply numerators and denominators separately
  • Example: 1/2 × 3/4 = 3/8
• Division: invert and multiply
  • Example: 1/2 ÷ 3/4 = 1/2 × 4/3 = 2/3

Types of Fractions

• A proper fraction has a numerator that is less than the denominator, such as 1/2 or 2/3.
• An improper fraction has a numerator that is greater than or equal to the denominator, such as 3/2 or 5/5.
• A mixed number is a combination of a whole number and a proper fraction, such as 2 1/2 or 3 3/4.

Equivalent Fractions

• Equivalent fractions are fractions that have the same value but different forms, such as 1/2 = 2/4 = 3/6.
• They can be obtained by multiplying or dividing both the numerator and denominator by the same number.

Simplifying Fractions

• Simplifying a fraction involves reducing it to its simplest form by dividing both the numerator and denominator by their greatest common divisor (GCD).
• Example: 6/8 can be simplified to 3/4 by dividing both numbers by their GCD of 2.

Comparing Fractions

• Comparing fractions involves determining which fraction is larger or smaller.
• This can be done by converting fractions to equivalent fractions with the same denominator, or by comparing the numerators and denominators separately.

Operations with Fractions

• To add or subtract fractions, they must have a common denominator.
• Example: 1/4 + 1/4 = 2/4, and 2/3 - 1/3 = 1/3.
• To multiply fractions, multiply the numerators and denominators separately.
• Example: 1/2 × 3/4 = 3/8.
• To divide fractions, invert and multiply.
• Example: 1/2 ÷ 3/4 = 1/2 × 4/3 = 2/3.

This quiz covers the basics of fractions, including proper fractions, improper fractions, mixed numbers, and equivalent fractions. Learn to identify and work with different types of fractions.