# Scala Reduce vs Fold

There is only a subtle difference between `reduce` and `fold`. Fold requires an initial value, whereas reduce doesn’t need one.

Reduce example:
```
scala> (1 to 10).reduce(_ * _)
val res0: Int = 3628800
```

Fold example:
```
scala> (1 to 10).fold(0)(_ * _)
val res0: Int = 0

scala> (1 to 10).fold(1)(_ * _)
val res1: Int = 3628800
```

This is because `reduce` requires the operator to be both **commutative** and **associative**, whereas `fold` requires the operator to be **associative** only.

A reminder of some basic arithmetics concepts:

Commutative property:
\\[
a + b = b + c
\\]

Associative property:
\\[
(a + b) + c= a + (b + c)
\\]