How do I divide the fraction 3/4 by 2/5?

To divide by a fraction, you multiply by its reciprocal, which means you flip only the second fraction, never the first. So for 3/4 ÷ 2/5, keep 3/4 as it is, then flip 2/5 to 5/2 and change the division to multiplication: 3/4 × 5/2. Now multiply straight across, numerator times numerator and denominator times denominator: (3 × 5)/(4 × 2) = 15/8. Since 15 is bigger than 8, you can write it as the mixed number 1 and 7/8. The rule 'keep, change, flip' helps you remember: keep the first fraction, change the sign to multiply, flip the second fraction. Only the fraction after the division sign gets turned upside down.