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

  • $3\frac{3}{4}$ has the whole number 3 and the fraction $\frac{3}{4}$, 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

  • $\frac{15}{4}$ 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 $4\frac{6}{7}$ into a top heavy fraction

  • $4\times 7=28$

• Add the result to the numerator of the fraction part

  • $28+6=34$

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

  • $4\frac{6}{7}=\frac{34}{7}$

• You can also think of this as

$4\frac{6}{7}=4+\frac{6}{7}=\frac{28}{7}+\frac{6}{7}=\frac{28+6}{7}=\frac{34}{7}$

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

• Divide the numerator by the denominator

  • For example, to convert $\frac{22}{3}$ into a mixed number 

  • $22÷3=7$ remainder $1$

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

• The fraction part is the remainder over the denominator

  • $\frac{22}{3}=7\frac{1}{3}$

• You can also think of this as

$\frac{22}{3}=\frac{21+1}{3}=\frac{21}{3}+\frac{1}{3}=7+\frac{1}{3}=7\frac{1}{3}$