Equivalent Fractions
Same amount, different outfit
Here is a fact that feels like a magic trick the first time: 1/2, 2/4, 3/6, and 50/100 are all the exact same amount. Same spot on the number line, same amount of pizza. They are one number wearing different outfits.
Why it works
Take half a sandwich and cut each half into 2. Now you have 2 pieces out of 4 total. You did not gain or lose any sandwich, you just made more, smaller pieces. Cutting every piece into the same number of smaller pieces changes the labels but not the amount.
Multiply (or divide) the top and bottom by the same number, and the fraction's value does not change. 1/2 with top and bottom times 3 becomes 3/6. Same amount, smaller pieces, more of them.
Going the other direction is called simplifying. If top and bottom share a common factor, divide both by it. 6/8: both divide by 2, giving 3/4. Simplifying does not shrink the amount, it just uses the fewest pieces possible. 3/4 is easier to picture than 75/100, and they are identical.
To find an equivalent fraction, ask: "What did the bottom get multiplied or divided by?" Then do the exact same thing to the top. Bottom went from 4 to 12? That is times 3, so the top gets times 3 too.