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Chapter 3: Problem 78

Evaluate the expression. $$10-[4.3+2(6.4 \div 8)]$$

Short Answer

Expert verified
The expression '10 - [4.3 + 2(6.4 梅 8)]' evaluates to 4.9.

Step by step solution

01

Identify and perform operations within parentheses.

The first operation within the parentheses involves the division of 6.4 by 8. This results in 0.8.
02

Complete the Parentheses operation.

Add the result from step 1 (0.8) to 4.3, which results in 5.1.
03

Perform subtraction operation.

Subtracting the result from step 2 (5.1) from 10 gives 4.9. This is the final result of the entire expression.

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Key Concepts

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

Parentheses
Parentheses are crucial in understanding how to solve math problems because they tell us what operations to do first. In any expression, the operations inside the parentheses should be completed before moving on to other parts of the equation. For example, in the exercise \(10 - [4.3 + 2(6.4 \div 8)]\), we first look inside the brackets and deal with the operations we find there.

This means we start with \(6.4 \div 8\) since division is the first operation inside those parentheses. Always remember, those tiny curved lines are there for a reason: they help organize operations step by step. Let the parentheses guide you, and you鈥檙e sure to solve complex equations correctly.
Division
Division is one of the fundamental operations in math and appears in many expressions, including this one: \(6.4 \div 8\). This operation asks, "How many times does 8 fit into 6.4?" In more straightforward terms, you're splitting 6.4 into groups of 8.

When you divide 6.4 by 8, you end up with 0.8. This result is essential because it feeds directly into the next steps of solving the expression. It's crucial to handle division carefully, as it often directly affects the accuracy of your future calculations within the problem.

A great tip is to always double-check your division, especially when decimals are involved, like in this example.
Addition
Addition is one of the simplest and most fundamental arithmetic operations, represented by a plus sign (+). In the expression, once we have solved the division within the parentheses, and simplified it to \(6.4 \div 8 = 0.8\), we then add this result to 4.3.

Adding 0.8 to 4.3 is straightforward: you simply combine the two numbers. The result is 5.1, which replaces the expression inside the parentheses.

Remember, addition is the process of bringing together numbers to get a total sum. Make sure the numbers are aligned correctly, especially when dealing with decimals, for accurate results.
Subtraction
Subtraction is all about taking one quantity away from another, represented by a minus sign (-). Once you've finished all the operations inside the parentheses in the given expression, you are left with a subtraction to perform.

Specifically, after simplifying within the parentheses to get 5.1, you subtract this from 10, as shown: \(10 - 5.1\). When you subtract 5.1 from 10, it results in 4.9.

Think of subtraction as finding the difference between numbers, like removing one part from a whole. Ensuring you subtract correctly, especially considering place value and decimals, will lead you to the correct final result.

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