Fraction Division
Dividing by a fraction means flipping the divisor and multiplying. 3/4 ÷ 1/3 asks how many times 1/3 fits inside 3/4. Sharing 3/4 of a pizza in 1/3 pieces gives 2 full pieces and a little more. Move the numerators and denominators and the bar model shows why flip-and-multiply works.
Dividing by a fraction asks how many times the second length sits inside the first. If you swap the top and bottom of the divisor and multiply, you get that same count without lining pieces on a bar. The flip is not a trick. It is the path that writes how many groups as a multiplication. You move the numerators and denominators with the sliders because that count changes when the lengths change.
The top two sliders are the numerator and denominator of the fraction being divided. The bottom two are the numerator and denominator of the fraction you divide by. At the top of the picture a question asks how many times the second fraction sits inside the first. The outline bar at the top is the whole 1. The next bar is painted blue only as far as the dividend fraction, with tick lines that cut the whole bar into as many parts as that denominator. The gold pieces below are the divisor length and are numbered from 1. A leftover piece is painted short and green, with the leftover length written to two decimal places. A dashed line drops from where the blue bar ends. At the bottom the division equation sits next to the same work written as multiply-by-the-flipped-divisor. Change the sliders and the lengths and piece counts are drawn again. The pieces sit at those lengths; they do not travel across the screen.
If you think you can divide the top numbers by the top numbers and the bottom numbers by the bottom numbers, you get a value that does not match the count on the bar. The method is to swap top and bottom on the divisor only, then multiply. If you flip the fraction being divided, the question itself changes. When you divide by a whole number, you first write that number as 1 over it after treating it as a fraction, then flip. Leave the practice items closed until you know which fraction flips. Which fraction you flip, and whether you multiply or divide, comes first.