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In mathematics, parentheses are used to group parts of an expression that should be calculated first. When you see an expression like \(12 + 7(4 + 3)\), the order of operations tells us to start with the parentheses. This is part of the PEMDAS/BODMAS rule, which stands for Parentheses (or Brackets), Exponents (or Orders), Multiplication and Division (left to right), Addition and Subtraction (left to right).

By performing the calculation inside the parentheses first, we simplify the math. In our example, within the parentheses \((4+3)\), we add 4 and 3 together to get 7. This makes the expression easier to handle: \(12 + 7(7)\). Parentheses help clarify which operations need priority, guiding us to the correct solution.

Once we have dealt with parentheses, the next operation in PEMDAS/BODMAS is multiplication. Consider the expression now at \(12 + 7(7)\). Here, \(7(7)\) signifies that we need to multiply 7 by 7.

Multiplication is a quick way to add a number repeatedly. Essentially, multiplying 7 by 7 is like adding 7, seven times. This gives us 49: \(7 \times 7 = 49\). It's important to complete any multiplication before moving on to other operations, ensuring the proper mathematical order is respected. This changes our expression to \(12 + 49\).

The last step in our order of operations is addition. With multiplication complete, the expression \(12 + 49\) leaves us only with simple addition.

Addition means calculating the total when two or more numbers are combined. Here, when you add 12 to 49, you get 61. So, \(12 + 49 = 61\).

• This step might seem straightforward, but it’s crucial to do it last to avoid errors.
• Remember, in PEMDAS/BODMAS, addition is among the final operations unless specified otherwise.

In large expressions, focusing on each step will help you reach the correct answer easily.