$\begin{array}{l}\left(-2 \frac{1}{8}\right)+\left(-3 \frac{1}{2}\right)+(+5)+(+1.125)+ \\ \left(+4 \frac{1}{2}\right)\end{array}$
Answer (2)
After converting mixed numbers to decimal form and grouping terms, the total sum of the expression ( − 2 8 1 ) + ( − 3 2 1 ) + ( + 5 ) + ( + 1.125 ) + ( + 4 2 1 ) is calculated to be 5 .
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Convert all mixed numbers to decimal form.
Group the positive and negative terms.
Calculate the sum of the negative terms: − 2.125 − 3.5 = − 5.625 .
Calculate the sum of the positive terms: 5 + 1.125 + 4.5 = 10.625 . The final result is 5 .
Explanation
Problem Analysis and Setup We are asked to evaluate the arithmetic expression:
( − 2 8 1 ) + ( − 3 2 1 ) + ( + 5 ) + ( + 1.125 ) + ( + 4 2 1 )
To solve this, we will convert all terms to decimal form and then add them together.
Converting to Decimals First, convert the mixed numbers to decimals:
− 2 8 1 = − 2 + ( − 8 1 ) = − 2 − 0.125 = − 2.125
− 3 2 1 = − 3 − 0.5 = − 3.5
4 2 1 = 4 + 0.5 = 4.5
So the expression becomes:
( − 2.125 ) + ( − 3.5 ) + 5 + 1.125 + 4.5
Adding the Terms Now, we add the numbers together:
− 2.125 − 3.5 + 5 + 1.125 + 4.5
Group the negative and positive terms:
( − 2.125 − 3.5 ) + ( 5 + 1.125 + 4.5 )
Add the negative terms:
− 2.125 − 3.5 = − 5.625
Add the positive terms:
5 + 1.125 + 4.5 = 10.625
Now, add the sum of the negative terms and the sum of the positive terms:
− 5.625 + 10.625 = 5
Final Result Therefore, the final result of the expression is 5.
Examples
This type of arithmetic problem is useful in everyday situations such as balancing a checkbook, calculating expenses, or determining profit in business. For example, if you spent $2.125 on coffee, $3.5 on lunch, received $5 as a gift, earned $1.125 from selling an item, and received $4.5 as payment for a task, the calculation above would tell you your net gain or loss.
