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Division is one of the four basic operations in arithmetic. It involves splitting a number into equal parts. In the context of our example, division helps determine how many times one number is contained in another. To perform the division in the exercise, you take 42 and divide it by 7. The result, 6, represents how many times 7 fits into 42.

To do this calculation by hand, you can think of division as repeated subtraction. You would repeatedly subtract 7 from 42 until you reach zero, counting how many times you performed the subtraction. This count is the quotient, which is 6 in this instance.

• Remember, division is the opposite of multiplication.
• It is essential to divide first in operations involving both division and subtraction, following the order of operations.
• The division is complete when there is no remainder left, which means you've evenly divided the original number.

Subtraction is another fundamental arithmetic operation. It involves taking one quantity away from another. This operation is used to determine the difference between numbers. In the exercise above, once the division is complete and we have the simplified expression 6 - 6, subtraction is the next step.

In this case, you subtract 6 from 6.

• Start with the minuend, which is the first number in the expression.
• Subtract the subtrahend, which is the second number.
• The result is the difference, which, here, is 0.

Subtraction can be checked by adding, where you add the subtrahend back to the difference to see if you get the original minuend.

The order of operations is a set of guidelines that determines the sequence in which arithmetic operations are performed. These guidelines ensure that everyone solves expressions consistently and correctly. An easy way to remember the correct order is by using the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

In our exercise example, we focused on division and then subtraction. According to PEMDAS, division should occur before subtraction. This is because division is prioritized higher than subtraction in the list of operations.

• Always solve operations inside parentheses first, though our example didn't have any.
• Remember, when both multiplication and division or addition and subtraction appear together, execute from left to right.
• Following the order of operations ensures accuracy and consistency across different mathematical problems.

Understanding the order of operations helps combat confusion and errors when simplifying complex expressions.