Converting Back and Forth

To turn a mixed number into an improper fraction, multiply the whole number by the denominator, add the numerator, and keep the same denominator.

Take 3 and 2/5. Multiply 3 by 5 to get 15, add 2 to get 17, so the answer is 17/5.

To go the other way, divide the numerator by the denominator. The quotient becomes the whole number and the remainder becomes the new numerator, sitting over the same denominator.

Why bother switching forms at all? Because each form is built for a different job. The mixed number tells you the size at a glance — 17/5 is hard to picture, but 3 and 2/5 clearly sits just past three. The improper fraction is the form that calculators and algebra prefer, because a single numerator over a single denominator multiplies and divides cleanly. Knowing how to flip between them on demand is what makes every later operation feel easy instead of fiddly.