91Ó°ÊÓ

Substitution in expressions is a crucial concept in algebra, where we replace variables with actual numerical values to simplify an expression or solve an equation. This method allows us to evaluate expressions for specific variable values, leading to a clearer understanding of the problem at hand. For the exercise, you needed to evaluate the expression \( x \div 4 \) when \( x = -52 \). To achieve this, we substituted \( x \) with \(-52\). This substitution transforms the original expression into \( -52 \div 4 \), making it ready for further calculation. When practicing substitution, always ensure you replace every instance of the variable with its given value. This step is essential to maintain the integrity of the expression and obtain an accurate solution.

Understanding negative numbers and their operations is fundamental in mathematics, especially when dealing with division. When you divide or multiply numbers, the sign of the result depends on the signs of the numbers involved. For division, the general rules are:

• If both numbers have the same sign, the result is positive.
• If the numbers have different signs, the result is negative.

In this exercise, \(-52\) is a negative number and it is being divided by a positive number (4). Because the signs are different, the division result is negative. This led to the final answer \(-13\). Always remember these sign rules, as they are widely applicable in both straightforward and complex mathematical problems.

The concept of absolute value helps us understand how far a number is from zero, without considering its direction (positive or negative). When dividing, it is often easier to first consider the absolute values of numbers, calculate the division, and then apply the sign rules to the final result.

For the expression \( -52 \div 4 \), we first took the absolute value of \(-52\), which is \(52\). We then divided \(52\) by \(4\), which equals \(13\). After determining the quotient using the absolute values, we returned to the original signs of the numbers to establish the sign of the final result, which was negative. Using absolute values simplifies calculations and helps avoid common errors when dealing with negative numbers.