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Magazine Chapter 1: Problem 58
Perform the operations. $$ -24-(-28)-48-44 $$
Short Answer
Expert verified
The result of the operations is \(-88\).
Step by step solution
01
Rewrite the Expression
Start by rewriting the expression to simplify it. The given expression is \(-24 - (-28) - 48 - 44\). Recognize that subtracting a negative number is equivalent to adding its positive counterpart. Therefore, \(-24 - (-28)\) becomes \(-24 + 28\). The rewritten expression is \(-24 + 28 - 48 - 44\).
02
Perform the First Addition
Next, perform the addition \(-24 + 28\). Since \(-24\) and \(28\) have different signs, subtract the smaller absolute value from the larger absolute value. The absolute difference is \(28 - 24 = 4\). The sign of the result takes the sign of the larger absolute value, which is \(28\). Therefore, \(-24 + 28 = 4\).
03
Subtract the Next Number
Take the result from Step 2, which is \(4\), and subtract \(48\) from it. Since \(4 - 48\) involves subtracting a larger number from a smaller number, find the absolute difference \(48 - 4 = 44\). The result will have a negative sign, thus \(4 - 48 = -44\).
04
Subtract the Last Number
Take the result from Step 3, which is \(-44\), and subtract \(44\) from it. Subtracting another \(44\) from \(-44\) yields \(-44 - 44\). Since both numbers are negative, add their absolute values and keep the sign negative. The result is \(-44 - 44 = -88\).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Subtraction of Integers
Subtraction might seem tricky when dealing with negative numbers, but with a little bit of guidance, it becomes straightforward.
When subtracting integers:
- If you subtract a negative number, imagine it as adding the corresponding positive number. For example, subtracting a negative (-28) from another (-24) becomes an addition: (-24) - (-28) = (-24) + 28.
- When finding the difference between numbers with different signs, such as 4 (from Step 2's result) minus 48, determine which number has the larger absolute value.
- This difference determines the result's sign. Use the formula: "larger absolute value minus smaller absolute value". For example, 4 - 48 results in -44 because 48 (larger absolute value) minus 4 equals 44, with the sign from 48.
Addition of Integers
Adding integers can be simpler if we use some basic rules. Here are key points to remember:
- When integers with different signs are added, the absolute values are compared. Subtract the smaller absolute value from the larger one.
- The resulting number takes the sign of the integer with the larger absolute value. For instance, when adding -24 and 28, calculate 28 - 24. The result is 4, since 28 has a larger absolute value than 24, the answer also takes the positive sign.
- If the integers have the same sign, simply add them together and keep the sign. For example, -44 + (-44) becomes -88.
Order of Operations
In mathematics, the order of operations is crucial to correctly solving expressions, especially those including integers.
Order of operations often follows the PEMDAS/BODMAS rule:
- P (Parentheses), B (Brackets)
- E (Exponents)
- MD (Multiplication & Division) evaluated from left to right
- AS (Addition & Subtraction) evaluated from left to right
