What is the simplified value of the expression below?
[tex]$1.6(-4.5-(-10.2)+4)$[/tex]
A. -29.92
B. -17.12
C. 15.52
D. 29.92
Answer (2)
Simplify the expression inside the parenthesis: − 4.5 − ( − 10.2 ) + 4 = 9.7 .
Multiply the result by 1.6: 1.6 × 9.7 = 15.52 .
Compare the result with the given options.
The simplified value of the expression is 15.52 .
Explanation
Understanding the Problem We are asked to simplify the expression 1.6 ( − 4.5 − ( − 10.2 ) + 4 ) and choose the correct answer from the options.
Simplifying the Parenthesis First, we simplify the expression inside the parenthesis: − 4.5 − ( − 10.2 ) + 4 = − 4.5 + 10.2 + 4 = 5.7 + 4 = 9.7
Multiplying by 1.6 Next, we multiply the result by 1.6: 1.6 × 9.7 = 15.52
Final Answer Finally, we compare the result with the given options and choose the correct one. The simplified value of the expression is 15.52.
Examples
Understanding how to simplify expressions like this is useful in many real-life situations. For example, if you are calculating the total cost of items with discounts and taxes, you need to simplify the expression to find the final amount you have to pay. This also applies when you are managing a budget, where you need to calculate income, expenses, and savings. Simplifying expressions helps you make informed financial decisions.
The simplified value of the expression 1.6 ( − 4.5 − ( − 10.2 ) + 4 ) is 15.52 , corresponding to option C. We simplified the expression inside the parentheses and then multiplied by 1.6 .
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