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Chapter 1: Problem 36

In Exercises \(1-72\), compute the value of each expression. $$4-7-2+3$$

Short Answer

Expert verified
The value of the expression is -2.

Step by step solution

01

- Identify the operations

The expression contains addition and subtraction operations: \(4 - 7 - 2 + 3\).
02

- Perform the operations from left to right

Mathematically, when only addition and subtraction are present, perform the operations from left to right. First, calculate: \(4 - 7 = -3\).
03

- Continue with the next operation

Using the result from Step 2, calculate: \(-3 - 2 = -5\).
04

- Complete the final operation

Using the result from Step 3, calculate: \(-5 + 3 = -2\).

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Key Concepts

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

Addition and Subtraction
When solving arithmetic expressions, two of the most common operations you will perform are addition and subtraction. These operations allow you to manipulate numbers to get the desired result. Adding two numbers means you are putting them together to get a larger number. Subtracting one number from another means you are taking away part of the number and making it smaller.

For instance, in the example from the exercise, you see both operations: 4 - 7 - 2 + 3. Each of these signs tells you to perform either an addition or a subtraction to the numbers that follow.
Order of Operations
In mathematics, the order in which you perform operations is very important. This is often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (left to right), and Addition and Subtraction (left to right).

However, when only addition and subtraction are involved, as in this exercise, you don't need to worry about the other operations. What is crucial, though, is performing the addition and subtraction correctly from left to right.

This means you will solve the expression in the sequence you see it: first subtraction, then another subtraction, and finally, an addition, ensuring each step follows the preceding one accurately.
Left to Right Calculation
Solving arithmetic problems from left to right ensures you follow the correct sequence of operations. In our example, the expression 4 - 7 - 2 + 3 needs to be handled one step at a time, starting from the leftmost operation and moving towards the right.

Let's break it down:
  • First, calculate 4 - 7. This gives you -3.
  • Next, use this result (-3) and continue with the next operation: -3 - 2. This results in -5.
  • Finally, take the result (-5) and add 3: -5 + 3, which equals -2.
By following the operations from left to right, it ensures that each calculation builds on the previous result, leading to an accurate answer.

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Most popular questions from this chapter

In Exercises \(73-84\), evaluate the given expression. $$7-3 \cdot 5-1$$

Evaluate the given expression. Remember to follow the order of operations. $$(30-5)(4-2)$$

In Exercises \(73-84\), evaluate the given expression. $$|-8+6-5|-8+6-5$$

A helicopter is hovering at an altitude of 600 ft above sea level directly above a submarine that is submerged at a depth of 128 ft below sea level. What is the distance between the helicopter and the submarine?

Evaluate the given expression. Remember to follow the order of operations. $$4+\\{3+5[2+2(3+1)]\\}$$
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