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Chapter 2: Problem 4

For Exercises \(2-7,\) simplify. $$-34+13$$

Short Answer

Expert verified
-21

Step by step solution

01

Identify the Numbers

The numbers to be simplified are -34 and 13.
02

Combine the Numbers

Start by combining the numbers: \[-34 + 13\]
03

Calculate the Sum

To find the result, add the two numbers together: \[-34 + 13 = -21\]

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Key Concepts

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

Addition of Integers
Addition of integers is a fundamental concept in arithmetic. When dealing with integers, remember that they include both positive and negative numbers. To add two integers, you can follow these simple rules:
  • If the signs are the same, add their absolute values and keep the common sign.
  • If the signs are different, subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value.
For example, in our exercise with \( -34 + 13 \), different signs mean we subtract their absolute values: \(34 - 13 = 21\). Since 34 has a negative sign, the result is -21.
Negative Numbers
Negative numbers are numbers less than zero. They are often represented with a minus sign (鈭�). Understanding negative numbers is crucial for accurately performing basic arithmetic operations. Here are some tips:
  • When adding a negative number to a positive one, you are essentially subtracting the absolute value of the negative number from the positive number.
  • When both numbers are negative, their absolute values are added, and the result retains the negative sign.
For instance, in our exercise, \( -34 \) is a negative number being added to a positive number \( 13 \). By understanding that \( -34 \) can be seen as 'subtracting 34', it helps clarify the operation: \( -34 + 13 \) essentially means 'subtract 34 from 13', yielding \( -21 \).
Basic Arithmetic
Basic arithmetic encompasses four primary operations: addition, subtraction, multiplication, and division. Mastery of these operations is essential for tackling more complex math problems. In this exercise, we focus on addition, especially involving integers. Here are some important points:
  • Read the signs carefully. Positive numbers add (move right on the number line) and negative numbers subtract (move left on the number line).
  • Integrate the rule of signs: if you're adding a positive and a negative number, subtract the smaller from the larger.
  • Simplify step-by-step. Break down the numbers part by part to avoid mistakes.
For -34 + 13, following the steps ensures clarity: note the signs, combine the numbers, and calculate the sum correctly. Thus, -34 added to 13 gives you \( -21. \)

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Most popular questions from this chapter

Fill in the blank with \(<,>,\) or \(=\) $$-(82) \square|46|$$

Perform the indicated operation. $$(-5)(-4)$$

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Divide the real numbers, if possible. $$\frac{-48}{-3}$$
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