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Chapter 1: Problem 35

In Exercises \(1-66,\) compute the value of each expression. $$-7+(-3)+5$$

Short Answer

Expert verified
-5

Step by step solution

01

- Evaluate the First Sum

Start by adding the first two numbers: a. Add \(-7\) and \(-3\).Using the rules of addition for negative integers, \((-7) + (-3) = -10\).
02

- Add the Result to the Last Number

Next, add the result from step 1 to the third number: a. Add \(-10\) and \(+5\).Using the rules of addition for a negative and positive number, \(-10 + 5 = -5\).

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Key Concepts

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

negative numbers
Negative numbers are numbers that are less than zero and are usually denoted by a minus sign in front of them. For example, in the expression \(-7 + (-3) + 5\), \(-7\) and \(-3\) are both negative numbers. Understanding how to work with negative numbers is crucial in mathematics.

When adding negative numbers, you are essentially combining their absolute values and giving the result a negative sign. For instance, adding \(-7\) and \(-3\):
  • The absolute values are 7 and 3.
  • Adding these gives 10.
  • Attaching the negative sign back results in \(-10\).

Negative numbers can seem tricky at first, but with practice, using them becomes second nature.
integer operations
Integer operations include addition, subtraction, multiplication, and division involving whole numbers. In this exercise, we're focusing on addition. Knowing the rules for adding positive and negative integers helps simplify complex problems. Here are some quick tips:
  • When adding two positive numbers, the result is always positive. Example: \(2 + 3 = 5\).
  • When adding two negative numbers, add their absolute values and place a negative sign before the result. Example: \(-4 + (-2) = -6\).
  • When adding a positive number to a negative number, subtract the smaller absolute value from the larger one, and assign the sign of the number with the larger absolute value to the result. Example: \(-5 + 3 = -2\).

Let's revisit our problem: \(-7 + (-3) + 5\)
  • We added \(-7\) and \(-3\) to get \(-10\).
  • Then, \(-10\) was added to \(+5\), resulting in \(-5\).
Practicing these rules helps you gain confidence and proficiency in solving integer-based problems.
step-by-step solutions
Approaching mathematical problems with a step-by-step method prevents confusion and ensures accuracy. Let's break down our given problem using this approach.

Step 1: Start by evaluating the first sum:
  • Consider the first two numbers, \(-7\) and \(-3\). According to the rule of negative number addition, \((-7) + (-3) = -10\).

Step 2: Add the result from step 1 to the third number:
  • Now, we have \(-10\) from step 1. Next, add this to the third number which is \(+5\). Using the rule for adding a negative and a positive number, we get \(-10) + 5 = -5\).
By following these steps, we ensured that our final answer was accurate. Step-by-step solutions not only help in solving math problems effectively but also deepen your understanding of the process involved.

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