Final answer:
To divide fractions, multiply the first fraction by the reciprocal of the second fraction. The result of dividing 1/5 by 4/7 is 7/20. The answer can be checked by multiplying 7/20 by 4/7, which simplifies to 1/5.
Step-by-step explanation:
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. So, to divide 1/5 by 4/7, we multiply 1/5 by 7/4. Multiplying the numerators gives 1 * 7 = 7, and multiplying the denominators gives 5 * 4 = 20. Therefore, the result of dividing 1/5 by 4/7 is 7/20.
To check our answer, we can multiply 7/20 by 4/7. Multiplying the numerators gives 7 * 4 = 28, and multiplying the denominators gives 20 * 7 = 140. Simplifying the fraction 28/140 gives us 1/5, which confirms that our original division was correct.