Fractions | Mathematics for GCSE/IGCSE - Year 11 PDF Download

Basic Fractions

What is a fraction? 

• A fraction represents a part of a whole. 
• It is written as a/b, where a and b are whole numbers (integers).
  • The number on the top, a, is called the numerator.
  • The number on the bottom, b, is called the denominator.
• For example, 1/2 means splitting something into 2 parts and taking 1 of these parts.
  • Another example is 2/3, which signifies splitting something into 3 parts and taking 2 of these parts.
  • Similarly, 4/5 indicates splitting something into 5 parts and taking 4 of these parts.

How do I find equivalent fractions?

• "Splitting something into 2 parts and taking 1 of these parts" is equivalent to "splitting something into 4 parts and taking 2 of these parts". 
  • This equivalence demonstrates that 1/2 is equal to 2/4. 
  • Extending this concept, 2/4 is equivalent to 4/8, 8/16, or 3/6, and so on.
• Equivalent fractions represent the same amount, just expressed differently. 
• To create equivalent fractions, multiply both the numerator and denominator of a fraction by the same value. 
  • For example, 5/6 is equivalent to  and so forth.
  • Every fraction has an infinite number of equivalent fractions. 
• To simplify a fraction to its "simplest" form, divide both the numerator and denominator by the largest whole number that divides into both (the "common factor"). 
  • For instance,
    
    

How do I find a fraction of an amount?

• When calculating a fraction of a quantity, there are several methods to consider:

Method 1: Division and Multiplication

• To find a fraction of an amount, divide the amount by the denominator and then multiply the result by the numerator.
• For example, to calculate 2/5 of 60, divide 60 by 5 to get 12, then multiply by 2 to get 24.

Method 2: Converting Fractions to Decimals

• If you can convert fractions to decimals, this method involves changing the fraction to a decimal and then multiplying it by the amount.
• For instance, to find 1/4 of an amount, you would multiply the amount by 0.25.

Method 3: Multiplying Fractions

• This method requires you to express both numbers as fractions and then multiply them together to find the desired fraction of a quantity.
• For example, To determine
  • To determine

Mixed Numbers & Top Heavy Fractions

What are mixed numbers & top heavy fractions?

• Mixed Numbers: A mixed number consists of a whole number part and a fraction part. For example,  has the whole number 3 and the fraction 3/4,  representing "three and three quarters".
• Top Heavy Fractions: Also known as improper fractions, top heavy fractions have a numerator larger than the denominator. For instance, 15/4 means "fifteen quarters".

Turning mixed numbers into top heavy fractions

• Multiply the whole number by the denominator (whole number × denominator).
• Add the result to the numerator.
• Express the new value as the numerator over the same denominator.

Turning top heavy fractions into mixed numbers

• Divide the numerator by the denominator to obtain the whole number part.
• Use the remainder as the new numerator.
• Keep the original denominator.