Dividing Fractions

For example:

$$ \dfrac{2}{5} \div \dfrac{3}{4}=?$$

• Step 1:
  Change the division sign (÷) to multiplication (×)
• Step 2:
  Flip the second fraction upside down (find its reciprocal): $\dfrac{3}{4}$ becomes $\dfrac{4}{3}$ $$\dfrac{2}{5} \div \dfrac{3}{4}=\dfrac{2}{5} \times \dfrac{4}{3}$$
• Step 3:
  Multiply the numerators: $2 \times 4 = 8$
  Multiply the denominators: $5 \times 3 = 15$
  So the answer is $\dfrac{8}{15}$

🌟 Exam Tip: Remember “Keep, Change, Flip”

Keep the first fraction, change the sign, flip the second fraction!

🔮 How to Flip a Whole Number:

When you divide a fraction by a whole number, you need to flip the whole number.

To do this, just view the whole number as a fraction over 1, then flip it.

For example:

$$ \dfrac{27}{30} \div 6=?$$

• Step 1:
  Change the division sign (÷) to multiplication (×)
• Step 2:
  Flip the whole number(find its reciprocal): $6$ becomes $\dfrac{1}{6}$ $$\dfrac{27}{30} \div 6=\dfrac{27}{30} \times \dfrac{1}{6}$$
• Step 3:
  Simplifying before multiplying makes your calculation easier and prevents mistakes. $$\dfrac{27}{30} = \dfrac{9}{10}$$
• Step 4:
  Multiply and get the answer: $$ \frac{9}{10} \times \frac{1}{6} = \frac{9}{60} = \frac{3}{20} $$

🌟 Exam Tip to Divide a Whole Number:

When you divide by a whole number, just write the number as a fraction over 1, turn it upside down, and multiply as usual.