91Ó°ÊÓ

Division is one of the fundamental arithmetic operations where we determine how many times one number is contained within another. In mathematical terms, division is the process of finding how many equal groups can be formed from a number.
For example, if you have 12 candies and you want to divide them among 6 friends, each friend gets 2 candies. This is expressed as 12 divided by 6 equals 2, or in mathematical notation, \( 12 \div 6 = 2 \).

When solving equations, division is performed after parentheses and exponents, but before addition and subtraction, according to the order of operations. It is crucial to tackle each operation carefully to avoid errors in your calculations. Always remember: Left to right applies to both division and multiplication in an equation.

Multiplication is all about adding the same number repeatedly. When you multiply, you're calculating the total of one number added a certain number of times. For example, multiplying 3 by 4 (\( 3 \times 4 \)) means you add 3 four times: \( 3 + 3 + 3 + 3 = 12 \).
This operation helps simplify repeated addition and works as a shortcut to find totals quickly.

When dealing with order of operations, multiplication comes at the same level as division. This means when you encounter both multiplication and division in an equation, you process them from left to right. As with our problem, this meant multiplying after dividing: \( 2 \cdot 2 = 4 \), which follows after \( 12 \div 6 = 2 \). Skipping steps or doing them out of order can lead to different and incorrect results.

Subtraction is used to find the difference between two numbers, essentially the process of removing objects from a group. If you have 10 apples and you give away 3, subtraction helps determine how many apples remain: \( 10 - 3 = 7 \).
It’s straightforward but essential for solving problems involving change or decrease.

In the context of the order of operations, subtraction is performed after multiplication and division. This ensures that all multiplication and division have been addressed in the equation before tackling subtraction. As shown in the problem, once we've calculated the multiplication result, we move on to the final step of subtraction, \( 4 - 22 = -18 \). This order ensures accuracy in simplifying expressions.