Mixed Numbers & Improper Fractions (SQA National 5 Maths): Revision Note

Converting between mixed numbers & improper fractions

What are mixed numbers & improper fractions?

• A mixed number has an integer part and a fraction part

  • has the whole number 3 and the fraction , meaning “three and three quarters”

• An improper fraction is also known as a top-heavy fraction

• An improper fraction is a fraction where the numerator is bigger than the denominator

  • means “fifteen quarters”

• Any fraction that is greater than 1 can be written as either a mixed number or an equivalent improper fraction

How do I convert a mixed number into an improper fraction?

• Multiply the integer part by the denominator of the fraction part

  • For example, convert into a top heavy fraction

  • 

• Add the result to the numerator of the fraction part

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• Write the 'new' numerator over the same denominator and ignore the integer part

  • 

• You can also think of this as

How do I convert an improper fraction into a mixed number?

• Divide the numerator by the denominator

  • For example, to convert  into a mixed number 

  • remainder 

• The integer part of the mixed number is the whole number

• The fraction part is the remainder over the denominator

  • 

• You can also think of this as