Chapter 2: Problem 42
Add. $$-60+18+(-40)+(-12)+93$$
Short Answer
Expert verified
Answer: The result is \(-1\).
Step by step solution
01
Identify the positive and negative numbers
In the given expression, identify the positive numbers and the negative numbers. Positive numbers: 18 and 93; Negative numbers: -60, -40, and -12.
02
Add the positive numbers together
Add the positive numbers together: \(18 + 93 = 111\)
03
Add the negative numbers together
Add the negative numbers together: \(-60 + (-40) + (-12) = -112\)
04
Add the sum of the positive numbers to the sum of the negative numbers
Add the sum of the positive and negative numbers together: \(111 + (-112) = -1\)
So the final result is:
$$-60 + 18 + (-40) + (-12) + 93 = -1$$
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Positive and Negative Numbers
Understanding positive and negative numbers is crucial in arithmetic. Positive numbers are those without any sign or with a '+' sign and represent quantities we have. Negative numbers, on the other hand, have a '-' sign and represent a deficit or loss. Visualizing a number line can be helpful, where numbers to the right of zero are positive, and numbers to the left are negative.
When we add a positive number, we move to the right on the number line. Conversely, adding a negative number means moving to the left. For instance, if we start at -60 and add 18, we are effectively moving 18 units to the right towards zero. In practical situations, positive and negative numbers can represent profits and debts, altitudes above and below sea level, temperatures above and below freezing, and more.
When we add a positive number, we move to the right on the number line. Conversely, adding a negative number means moving to the left. For instance, if we start at -60 and add 18, we are effectively moving 18 units to the right towards zero. In practical situations, positive and negative numbers can represent profits and debts, altitudes above and below sea level, temperatures above and below freezing, and more.
Arithmetic Operations
Arithmetic operations include addition, subtraction, multiplication, and division. These operations follow certain rules and properties to correctly combine numbers. When dealing with addition, it's important to consider the commutative property, which states that numbers can be added in any order, and the associative property, which allows us to group numbers differently without changing the result.
Understanding properties of arithmetic operations helps us efficiently calculate sums or differences, especially when working with a mix of positive and negative numbers. For example, we can group all positive numbers and add them, as well as group all negative numbers and add them before combining the two results.
Understanding properties of arithmetic operations helps us efficiently calculate sums or differences, especially when working with a mix of positive and negative numbers. For example, we can group all positive numbers and add them, as well as group all negative numbers and add them before combining the two results.
Prealgebra
Prealgebra serves as a foundation for understanding algebraic concepts. It includes basic arithmetic and introduces variables, expressions, and the rules for manipulating these expressions. When working with prealgebra problems, like the one in our exercise, it is essential to understand the order of operations, the concept of absolute value, and the role of parentheses.
The correct order of operations must be followed to arrive at the right answer. In cases where we are only adding numbers, this order becomes less complex but doesn't diminish the importance of correctly grouping numbers based on their sign.
The correct order of operations must be followed to arrive at the right answer. In cases where we are only adding numbers, this order becomes less complex but doesn't diminish the importance of correctly grouping numbers based on their sign.
Calculating Sums
Calculating sums, particularly when combining positive and negative numbers, requires careful attention to their signs. To make the process clearer, one helpful tip is to rewrite the addition of a negative number as subtraction. For instance, adding -40 is the same as subtracting 40. This is especially useful in problems involving a mix of many positive and negative numbers.
To calculate the sum of numbers, first, add together all of the positive numbers for a subtotal. Do the same for the negative numbers, creating a negative subtotal. Lastly, combine the two subtotals to get the final total. Using this systematic approach can prevent errors in calculations and make dealing with larger sets of numbers more manageable.
To calculate the sum of numbers, first, add together all of the positive numbers for a subtotal. Do the same for the negative numbers, creating a negative subtotal. Lastly, combine the two subtotals to get the final total. Using this systematic approach can prevent errors in calculations and make dealing with larger sets of numbers more manageable.
