Mixed Numbers (SQA National 5 Applications of Mathematics): Revision Note

Mixed numbers

What are mixed numbers?

• 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”

• Numbers can be written using mixed numbers instead of decimals

  • e.g. $3\frac{1}{2}=3.5$

What are improper fractions?

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

  • $\frac{15}{4}$ means “fifteen quarters”

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

• 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?

• STEP 1
  Split the whole numbers into multiples of the denominator

  • e.g. Consider $3\frac{1}{2}$

    • 1 whole is equal to 2 halves

    • Therefore, 3 is equal to 3 × 2 = 6 halves

  • e.g. Consider $5\frac{2}{7}$

    • 1 whole is equal to 7 sevenths

    • Therefore, 5 is equal to 5 × 7 = 35 sevenths

• STEP 2
  Add the numerator of the fraction part

  • e.g. Consider $3\frac{1}{2}$

    • 6 halves and 1 half make 7 halves

    • $3\frac{1}{2}=\frac{7}{2}$

  • e.g. Consider $5\frac{2}{7}$

    • 35 sevenths and 2 sevenths make 37 sevenths

    • $5\frac{2}{7}=\frac{37}{7}$

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

• Divide the numerator by the bottom to get a whole number and a remainder

  • e.g. 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

  • $\frac{22}{3}=7\frac{1}{3}$