To divide 4 1/4 by 2 1/2, we first convert both mixed numbers to improper fractions:
4 1/4 = (4 * 4 + 1) / 4 = 17 / 4
2 1/2 = (2 * 2 + 1) / 2 = 5 / 2
Now, we can perform the division:
(17/4) ÷ (5/2) = (17/4) * (2/5)
To multiply fractions, we multiply the numerators together and the denominators together:
Numerator: 17 * 2 = 34
Denominator: 4 * 5 = 20
So, the result of the division is 34/20.
To write this as a mixed number, we find the whole number part and the fractional part:
Whole number part: 34 ÷ 20 = 1 (1 whole)
Remaining fraction: 34 % 20 = 14 (14/20)
Now, we simplify the fraction:
14/20 can be reduced to 7/10 by dividing both the numerator and denominator by their greatest common divisor, which is 2.
So, the final result is 1 7/10.