Final answer:
To divide 3/4 by 2/5, multiply 3/4 by the reciprocal of 2/5, which is 5/2, resulting in 15/8 or 1 7/8 as a mixed number.
Step-by-step explanation:
To divide 3/4 by 2/5, you need to multiply 3/4 by the reciprocal of 2/5. The reciprocal of a fraction is obtained by swapping its numerator and denominator. Thus, the reciprocal of 2/5 is 5/2.
Now, multiply 3/4 by 5/2 to find the answer:
3/4 × 5/2 = (3 × 5) / (4 × 2) = 15/8
This result can also be expressed as a mixed number:
15 ÷ 8 = 1 with a remainder of 7,
So the mixed number is 1 7/8.