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Chapter 1: Problem 58

Add. Do not use the number line except as a check. \(24+3.1+(-44)+(-8.2)+63\)

Short Answer

Expert verified
37.9

Step by step solution

01

Group Positive and Negative Numbers

First, identify and separate the positive and negative numbers in the expression. Positive numbers are: 24, 3.1, and 63. Negative numbers are: -44 and -8.2.
02

Add the Positive Numbers

Add all the positive numbers together: 24 + 3.1 + 63 = 90.1.
03

Add the Negative Numbers

Add all the negative numbers together: -44 + (-8.2) = -52.2.
04

Combine the Sums

Combine the sum of positive numbers with the sum of negative numbers: 90.1 + (-52.2) = 90.1 - 52.2 = 37.9.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Integer Addition
Integer addition is combining whole numbers, including positive and negative numbers. To master it, you need to understand how different signs (positive and negative) affect the sum.

Here are some tips on adding integers:
  • If the numbers have the same sign, simply add their absolute values, and keep the common sign.
  • If the numbers have different signs, subtract the smaller absolute value from the larger one, and keep the sign of the number with the larger absolute value.

For example, when adding 24 and -44, think of it as: 24 - 44 = -20. This is because 44 is larger in absolute value, and it is negative.
Similarly, adding -8.2 and 3.1 means subtracting 8.2 - 3.1 = 5.1, and keeping the negative sign, resulting in -5.1.
Decimal Addition
Decimal addition involves adding numbers that have a fractional part, like 3.1 or -8.2. Here鈥檚 how to handle it confidently:
  • Line up the decimal points of the numbers you鈥檙e adding to ensure accuracy.
  • Add digits starting from the rightmost side, just like with whole numbers, and carry over if necessary.

Consider the example from the exercise:
  • Step 2: Add positive decimals 24 + 3.1 + 63 by lining up decimal points.
  • This will give you 90.1.

Next, add the negative decimals:
  • Step 3: -44 + (-8.2) line them up and add to get -52.2.
  • The decimal point ensures that you are adding the numbers correctly in their respective place values.
Combining Positive and Negative Numbers
Once you've separately added all the positive and negative numbers, the final step is to combine these sums. This involves more than just arithmetic; it's about balancing positive and negative influences:
  • First, remember the line you've got so far: the positive sum was 90.1 and the negative sum was -52.2.
  • Combine these two results: 90.1 + (-52.2). Practically, this means you are subtracting because adding a negative is the same as subtracting.

Here鈥檚 a rule to follow: the final sign will be the sign of the larger absolute sum.
So, 90.1 - 52.2 = 37.9 positively.
This rule applies universally when combining mixed sign numbers. Add positive and negative numbers keeping their sign impact: positive numbers increase the sum, negatives decrease it.

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