Final answer:
To divide 2/5 by 1 4/5, we multiply the first fraction by the reciprocal of the second fraction. The result is 10/45.
Step-by-step explanation:
To divide 2/5 by 1 4/5, we need to convert the mixed number 1 4/5 into an improper fraction. This can be done by multiplying the whole number (1) by the denominator of the fraction (5) and adding the numerator (4) to get 9. We then rewrite the mixed number as an improper fraction: 1 4/5 = 9/5. Now we can divide: 2/5 ÷ 9/5.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 9/5 is 5/9. So, we have (2/5) x (5/9).
Multiplying the numerators (2 x 5) gives us 10, and multiplying the denominators (5 x 9) gives us 45. Therefore, 2/5 ÷ 1 4/5 = 10/45.