Problem 17 - Algebra A Combined Function

Question

Subtract. \(-44-27\)

Step-by-Step Solution

Answer

The solution is -71.

Step 1: Understanding the Problem

The problem requires us to subtract two numbers, -44 and 27.

Step 2: Rewriting the Expression

Subtracting a positive number is the same as adding its negative. Rewrite the expression as \(-44 - 27 = -44 + (-27)\).

Step 3: Applying the Rule for Adding Negative Numbers

When adding two negative numbers, combine their absolute values and keep the negative sign. In this case, combine 44 and 27.

Step 4: Calculate the Absolute Values

Add the absolute values: \(44 + 27 = 71\).

Step 5: Applying the Negative Sign

Since both original numbers were negative, the result of the addition should also be negative. Thus, \(-44 + (-27) = -71\).

Key Concepts

Subtracting Integers

When dealing with integers, subtraction can often be recalibrated as a problem of addition, which is especially useful when dealing with negative numbers. For example, if we need to solve \(-44 - 27\), it is important to first rethink the subtraction as adding a negative version of the second number.

• Rewrite the subtraction as addition: \(-44 - 27\) becomes \(-44 + (-27)\).
• This shift in perception helps simplify the problem and aligns with standard rules for addition.

Subtraction as a concept involves finding the difference between numbers, but in this scenario of integer operations, transforming the operation into addition can ease the process and reduce mistakes.

Adding Negative Numbers

Adding negative numbers can initially seem tricky, but it follows straightforward rules that, once understood, make the process simple. Let's break it down with our example of adding \(-44\) and \(-27\).

• When both numbers are negative, like in our case, you add their absolute values.
• Once the absolute values are summed up, remember to apply the negative sign to the total.

This means for \(-44 + (-27)\), you combine 44 and 27 to get 71, and then make the result negative, arriving at \(-71\). Remember, adding a larger negative number to a smaller one results in an even more negative number, which is key when handling such integer operations.

Absolute Value Calculation

The absolute value of an integer is the non-negative magnitude of the number, regardless of direction on the number line. In simpler terms, it's how far the number is from zero without considering whether it's on the left or right side of the number line. Here's how it works:

• The absolute value of a positive number is the number itself. For example, the absolute value of 27 is simply 27.
• For negative numbers, like \(-44\), the absolute value disregards the negative sign, turning it into 44.

In our calculation involving \(-44 + (-27)\), knowing the absolute values (44 and 27) allowed us to easily sum them to 71. This concept is crucial as it simplifies many steps when performing operations like addition and subtraction of negative numbers.