"A processing machine crushes 3 1/4 kilograms of dried fruits in 3/4 minutes.
What is the rate, in kilograms per minute, at which the machine crushes dried fruits?"
All you're doing here is finding the unit rate at which the machines crushes the fruit. This boils down to dividing the amount it can crush (3 + 1/4 kg) by the time it takes to do the crushing (3/4 min):
(3 + 1/4 kg) / (3/4 min)
We can omit the units, just remember everything is measured in kilograms per minute. So we want to simplify the expression,
(3 + 1/4) / (3/4)
Write the numerator as an improper fraction:
3 + 1/4 = 12/4 + 1/4 = 13/4
(since 12 = 3*4)
Then
(3 + 1/4) / (3/4) = (13/4) / (3/4)
Multiply this by 1 = 4/4. In other words, multiply both the numerator and denominator by 4. This eliminates the fractions in either part, and you get the answer:
(13/4) / (3/4) * 4/4 = (13/4 * 4) / (3/4 * 4) = 13/3
So in one minute, the machine can crush 13/3 kg ≈ 4.333 kg of dried fruit.