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When you see a math problem like \(75 \div (7+8) - 3\), it's important to know the right order to solve each part. This order is crucial because it ensures everyone gets the same answer. The order we're talking about is called the "Order of Operations." In math, we use the acronym PEMDAS to help us remember this order. It stands for:

• P: Parentheses first
• E: Exponents (like squares or powers)
• M/D: Multiplication and Division (from left to right)
• A/S: Addition and Subtraction (from left to right)

In our exercise, we start by simplifying the part inside the parentheses \((7 + 8)\). After that, we move on to any division or multiplication, before finally handling any addition or subtraction. This consistent order helps to avoid confusion and guarantees the right outcome.

Division is one of the four basic operations in mathematics, along with addition, subtraction, and multiplication. In this exercise, once we've dealt with the parentheses, we arrive at the expression \(75 \div 15 - 3\). Here, division comes before subtraction according to our order of operations. Performing division means figuring out how many times one number (the divisor) fits into another (the dividend). In this case, 15 fits exactly 5 times into 75. Imagine you have 75 candies, and you want to distribute them equally among 15 friends. Each friend would receive 5 candies. This is the practical visualization of \(75 \div 15 = 5\). Division lets us group things equally, helping us to simplify numbers and solve equations.

Subtraction is the process of taking one number away from another. It is a straightforward operation but very important in math. Once you've done the division in our exercise, you land on the expression \(5 - 3\).In subtraction, we're essentially counting backward or reducing a number, which in our case is 5, by taking away 3. Think of it like starting with 5 apples and eating 3 of them. You'll have 2 left. That's the outcome of \(5 - 3\).When solving equations, subtraction often helps in reducing problems down to their simplest forms. This solving technique is a basic skill that's vital in everyday mathematics and in more complex problems.