Same Amount, New Name

Cut a bar in half and shade one half: that is 1/2. Cut the same bar into 4 equal pieces instead, and the shaded part covers 2 of them, 2/4. Cut it into 6, and it covers 3, 3/6. Three names, one amount.

Top: 1 of 2 pieces. Middle: 2 of 4. Bottom: 3 of 6. The shaded amount is the same.

Look at what changed from 1/2 to 3/6: every piece was cut into 3, so there are 3 times as many pieces, and 3 times as many of them are shaded. The top and the bottom were both multiplied by 3. Multiplying the top and the bottom by the same number gives an equivalent fraction: a new name for the same amount.

It works for any fraction and any multiplier except 0: 2/3 is 4/6, and also 10/15. On a number line, equivalent fractions land on exactly the same point. What does not work is adding the same number to the top and the bottom: 1/2 with 1 added to each becomes 2/3, which is a bigger amount.