Mixed Numbers & Improper Fractions (Cambridge International IGCSE Maths)

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?

• Consider $5\frac{2}{7}$

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

  • 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

  • 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

  • For example, convert $\frac{22}{3}$ into a mixed number
  • $22\div3=7$ remainder $1$

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

• The fraction part is the remainder over the denominator

  • $\frac{22}{3}=7\frac{1}{3}$

Worked Example (a) Write $5\frac{3}{4}$ as an improper fraction.

Answer:

Split the whole number into quarters

1 whole is 4 quarters

5 wholes is 5 × 4 = 20 quarters

Add the quarters from the fraction

20 + 3 = 23 quarters

$\frac{23}{4}$

(b) Write $\frac{17}{5}$ as a mixed number.

Answer:

Divide the top by the bottom

17 ÷ 5 = 3 remainder 2

The final answer is 3, with 2 parts still left over

Leave the 3 as the whole number part and put the 2 over the original denominator of 5

$3\frac{2}{5}$