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Chapter 1: Problem 45

Find each sum without the use of a number line. $$3.5+(-45)+(-8.4)+72$$

Short Answer

Expert verified
The sum is \(22.1\).

Step by step solution

01

Simplify the Problem

Since this problem simply involves addition, it doesn't matter in which order the numbers are added. However, grouping positive and negative numbers together can help simplify the problem. Thus, separate the positive numbers from the negative numbers. \[3.5+72\] and \[(-45)+(-8.4)\]
02

Adding Up the Numbers

Now, add the separated positive and negative numbers together. You get \(3.5+72 = 75.5\) for the positive numbers, and for the negative numbers, the sum is \(-45 -8.4 = -53.4\). Remember, adding a negative number is equivalent to subtracting that number. Therefore, \(-45 + (-8.4)\) is the same as \(-45 - 8.4\).
03

Final Sum

Finally, sum the resulting numbers from step 2 which are 75.5 and -53.4. The operation will be \(75.5 +(-53.4)\) which is the same as \( 75.5 - 53.4 = 22.1\)

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