Dividing Fractions

🛎️ How to Handle Mixed Numbers in Division:

A mixed number is a number made up of a whole number and a fraction, for example,

$$2\dfrac{1}{3} = 2 + \dfrac{1}{3}$$

When dividing with mixed numbers, always convert them to improper fractions first before dividing.

For example,

$$2\dfrac{2}{5} \div \dfrac{2}{5}=?$$

• Step 1:
  Change the division sign (÷) to multiplication (×)
• Step 2:
  Convert the mixed number to an improper fraction:
  $$2\dfrac{2}{5} = \dfrac{2 \times 5 + 2}{5} = \dfrac{12}{5}$$
• Step 3:
  Flip the second fraction (find the reciprocal): $\dfrac{2}{5}$ becomes $\dfrac{5}{2}$ $$\dfrac{12}{5} \div \dfrac{2}{5} = \dfrac{12}{5} \times \dfrac{5}{2}$$
• Step 3:
  Multiply and simplify:
  $$\dfrac{12}{5} \times \dfrac{5}{2} = \dfrac{12 \times 5}{5 \times 2} = \dfrac{60}{10} = 6$$

❇️ Exam Tip to Divide Mixed Numbers:

Always turn mixed numbers into improper fractions before dividing. If you don’t convert first, your answer will be wrong!