Perform the following divisions and express the answers as fractions reduced to lowest terms.
2&5/10 ÷ 4&1/6 =
To divide 2&5/10 by 4&1/6, we first need to convert the mixed numbers to improper fractions.
2&5/10 can be rewritten as 2 + 5/10 = 2 + 1/2 = 2 * (10/10) + 1/2 = 20/10 + 1/2 = 21/10.
Similarly, 4&1/6 can be rewritten as 4 + 1/6 = 4 * (6/6) + 1/6 = 24/6 + 1/6 = 25/6.
Now we can divide 21/10 by 25/6 by multiplying the dividend by the reciprocal of the divisor:
(21/10) ÷ (25/6) = (21/10) * (6/25) = (21 * 6) / (10 * 25) = 126/250.
Finally, we can reduce the fraction 126/250 to lowest terms. The greatest common divisor (GCD) of 126 and 250 is 2, so we can divide both numerator and denominator by 2:
126/250 = (126/2) / (250/2) = 63/125.
Therefore, the division 2&5/10 ÷ 4&1/6 can be expressed as the fraction 63/125.