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Distribution in algebra is a fundamental concept that helps us simplify expressions by multiplying everything inside the parentheses by the term outside.

For example, with the expression \(12\left(\frac{5}{6} p\right)\), we use distribution to multiply the 12 by each term inside the parentheses.

Let’s go through the concept:

\(a(b + c) = ab + ac\), this means you multiply \(a\) with both \(b\) and \(c\).

In our example, we have a single term inside the parenthesis, \(\frac{5}{6} p\), that we will distribute 12 to:
\(12 \times \left(\frac{5}{6} p\right)\).

This step ensures that all parts of the expression are multiplied correctly and helps in breaking down complex equations.

Simplifying fractions is another crucial skill in algebra. It makes calculations easier and the expressions cleaner.

The process involves reducing the fraction to its smallest form so the numbers are easier to handle.

Here’s what we did in our problem:

• We started with \(\frac{12 \times 5}{6}\)
• Simplified it by multiplying the numerator: \(12 \times 5 = 60\)
• Then divided by the denominator: \(\frac{60}{6} = 10\)


To simplify fractions, always look for common factors in both the numerator and the denominator.
This helps in reducing the fraction to its simplest form, making it easier to work with.

Multiplication is a basic but essential operation in algebra. It involves combining equal groups to find out the total number of items.

For instance, in our example, we multiplied numbers and then included the variable:

• First, we multiplied the constant numbers:
\textrm{12} \times \frac{5}{6} = 10
• Next, we incorporated the variable:
\t10 \times p = 10p
The order of multiplication doesn’t matter (this is called the commutative property), as \(a \times b = b \times a\).

Multiplying correctly is key to simplifying expressions and solving equations accurately.