91Ó°ÊÓ

When simplifying expressions, it's essential to follow the order of operations. This ensures that everyone simplifies expressions the same way and gets the same result. The order of operations can be remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

In the given problem, there are no parentheses or exponents, so we move directly to multiplication and division. Multiplication comes before addition, which is why we must carry out the multiplications first before proceeding with the addition. Understanding and applying the order of operations correctly is crucial in getting the correct answer while simplifying any mathematical expression.

Multiplication is one of the basic arithmetic operations. In this problem, we have two multiplications to perform:

• First, multiply 4 and 7, which gives 28.
• Second, multiply 3 and 5, which gives 15.

These steps are the initial part of the order of operations in our expression \(4 \times 7 + 3 \times 5\). Performing these multiplications first clears up the path for the next steps, aligning with the PEMDAS rule, so when we come to the addition step, we're dealing with individual numbers rather than more complex expressions.

After completing the multiplications, we move on to the next step: addition. In our problem, we need to add the results of the two multiplications we've performed.

• We have 28 from multiplying 4 and 7.
• We have 15 from multiplying 3 and 5.

Adding these two results together, we get: \(28 + 15 = 43\).

This final step wraps up the simplification of the original expression, neatly following the prescribed order of operations. Always remember, addition comes at the end once all multiplications and divisions have been handled!