A coefficient is a number that multiplies a variable in mathematics. In the expression 5x, the coefficient is 5 because it tells you how many x's you have. In 3y, the coefficient is 3. Think of it like this: if x represents apples, then 5x means five groups of apples, and the coefficient 5 tells you how many groups.

Coefficients show up everywhere in algebra. In the equation 2a + 7b = 20, both 2 and 7 are coefficients. They're the numbers paired with the letters. When you see 4x² + 3x + 8, the coefficients are 4 and 3 (the 8 stands alone, so it's called a constant instead).

Scientists use coefficients too. A coefficient of friction measures how slippery two surfaces are against each other: ice on metal has a low coefficient of friction, which is why ice skates glide so smoothly. In chemistry, coefficients tell you how many molecules you need: in 2H₂O, the coefficient 2 means you need two water molecules.

Understanding coefficients helps you see patterns in math. If you're comparing 6x and 2x, you can quickly tell that the first expression is three times larger because 6 is three times 2. The coefficient gives you that information at a glance.