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The multiplication property is a foundational concept in mathematics that can simplify complex expressions. It states that you can distribute a factor across terms in an expression. In simpler terms, if you see a number being multiplied by a sum, you can perform the multiplication on each addend separately. For example, in the expression

• \(5 \cdot 3 + 5 \cdot 6\),

we can use the multiplication property to blaze through the first step of this problem. First, multiply 5 by 3, which gives us 15. Next, multiply 5 by 6, which results in 30.
Putting these together, we have transformed our problem by replacing the products, leading us to the expression:

• \(\frac{15+30}{7-2}\).

This method of multiplying each term separately helps in reducing a cluttered expression into a much simpler form. It's important as it not only organizes our calculations, but also lays the foundation for solving more complex problems.

Addition is straightforward once you understand how it fits into larger arithmetic operations. By learning to combine numbers efficiently, you can simplify expressions and find solutions faster. In our expression

• \(15 + 30\),

we simply add the two numbers together. So, 15 plus 30 equals 45.
Notice how addition helps in condensation. Where previously there were two terms, now there is only one number, 45, standing alone in the numerator. This clarity in calculations shapes our work, making it easier for the mind to follow the sequence of operations without getting lost.

• Addition compacts calculations,
• Reveals solutions quickly,
• Keeps expressions tidy.

Subtraction is the opposite operation of addition, and it can similarly tidy up expressions and equations. In our denominator, we begin with the expression

• \(7 - 2\).

By simply subtracting 2 from 7, we arrive at 5. This result simplifies our expression into:

• \(\frac{45}{5}\),

which is easy and ready for the final step of division.
Subtraction is a crucial tool; it reduces the number of elements we have to consider, shaping a straightforward path towards the solution. It, paired with multiplication and addition, plays a pivotal role in guiding us through calculations and confirming the balance and order of operations within expressions.