In this lesson, we'll walk through how the `getAmountOut` function in the UniswapV2 library calculates the amount of tokens coming out of a swap. Let's start by looking at the `getAmountOut` function. ```javascript // given an input amount of an asset and pair reserves, returns an equivalent amount of the other asset function getAmountOut(uint amountIn, uint reserveIn, uint reserveOut) internal pure returns (uint amountOut) { require(amountIn > 0 && reserveIn > 0 && reserveOut > 0, 'UniswapV2Library: INSUFFICIENT_INPUT_AMOUNT'); // NOTE: // x = token in // y = token out // dx = amountIn * 997 / 1000 // dy = dx * 997 / 1000 * yo // ---------- // xo * 1000 + dx * 997 // NOTE: dx * 997 uint amountInWithFee = amountIn.mul(997); // NOTE: dx * 997 * yo uint numerator = amountInWithFee.mul(reserveOut); // NOTE: xo * 1000 uint denominator = reserveIn.mul(1000).add(amountInWithFee); // NOTE: // dy = dx * 997 / 1000 * yo // ---------- // xo * 1000 + dx * 997 amountOut = numerator / denominator; } ``` In this function, we calculate the amount out, `amountOut`, using a formula that we previously derived. We denote `amountIn` as `dx` and `reserveOut` as `yo`, the amount of tokens that are coming out of the swap. We calculate the `amountInWithFee` by multiplying `amountIn` by 997 and dividing by 1000. We also have the numerator, which is `amountInWithFee` multiplied by `reserveOut` or `dx * 997 * yo`. The denominator is `reserveIn` multiplied by 1000 added to `amountInWithFee`. ```javascript // NOTE: xo * 1000 uint denominator = reserveIn.mul(1000).add(amountInWithFee); ``` We denote `reserveIn` as `xo`, the current reserve for the token going into the swap. The denominator translates to `xo * 1000 + dx * 997`. The `amountOut` is then calculated as the `numerator` divided by the `denominator`. ```javascript amountOut = numerator / denominator; ``` We can see that the code reflects the equation we derived: ```javascript // dx * 997 / 1000 * yo // ---------- // xo * 1000 + dx * 997 ``` We'll cover the rest of the code in our next lesson.