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Let's start with a core concept called fraction multiplication. Multiplying fractions is simpler than it seems. When you multiply two fractions, you multiply the numerators (the numbers on top) together and the denominators (the numbers on the bottom) together. Here's an example:

Suppose we have \( \frac{2}{3} \times \frac{4}{5} \).

You multiply the numerators: 2 * 4 = 8
You multiply the denominators: 3 * 5 = 15
So, \( \frac{2}{3} \times \frac{4}{5} = \frac{8}{15} \).

This method helps you combine fractions into one. In our exercise, we used fraction multiplication to simplify the terms.

Next is the commutative property of multiplication, a fundamental property in math, which states that the order in which you multiply numbers does not matter.

This means \( a \times b \) is the same as \( b \times a \).

In our exercise, we had \( \frac{5}{13} \times 57 \times \frac{13}{5} \).

We rearranged it using the commutative property:

\( \frac{5}{13} \times \frac{13}{5} \times 57 \).

Rearranging makes it easier to spot and simplify components of the expression. So, it's crucial to understand and use the commutative property while working with multiplication problems involving fractions.

Let's dive into simplifying expressions. Simplification involves making an expression easier to work with or solve. This often means reducing it to its simplest form.

In our exercise, we needed to simplify: \( \frac{5}{13} \times 57 \times \frac{13}{5} \).

First, by noticing and applying the commutative property: Rearranging \( \frac{5}{13} \times \frac{13}{5} \times 57 = 1 \times 57 \).

How did we get to 1? Because \( \frac{5}{13} \times \frac{13}{5} = 1 \). This is because the fractions cancel out each other as their numerator and denominator are reciprocals.

After that, multiplying by 1, which is straightforward: 1 times any number is that number itself. So, the simplified result is 57.

Remember to always look for parts of the fraction that can cancel out or reduce. This helps turn a complex expression into a simpler one.