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Chapter 10: Problem 8

Add. Do not use the number line except as a check. $$ -4+(-6) $$

Short Answer

Expert verified
-10

Step by step solution

01

- Understand the Numbers

Identify the numbers involved in the addition. We have -4 and -6, both of which are negative integers.
02

- Combine the Numbers

When adding two negative numbers, combine their absolute values and keep the negative sign. The absolute values of -4 and -6 are 4 and 6, respectively.
03

- Add the Absolute Values

Add the absolute values: 4 + 6 = 10.
04

- Apply the Negative Sign

Since both original numbers were negative, the result is also negative. Therefore, -4 + (-6) = -10.

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Key Concepts

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

negative integers
Negative integers represent numbers less than zero. They are usually denoted with a minus sign (-) in front. For example, in the exercise, -4 and -6 are negative integers. Negative numbers are useful in many areas of mathematics and real life, such as indicating temperatures below freezing or debts in finance. When you add two negative integers, like -4 and -6, you need to consider their absolute values to understand the effect they have on the sum.
absolute value
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always a non-negative number. For example, the absolute values of -4 and -6 are 4 and 6, respectively. The notation for absolute value is with two vertical bars: \( |x| \). So, \( |-4| = 4 \) and \( |-6| = 6 \). In the given problem, we use the absolute values to simplify the addition of negative integers.
integers addition
Adding integers involves combining their values. For the given example, -4 + (-6), follow these steps:
  • Identify the numbers and their signs.
  • Determine the absolute values: 4 and 6.
  • Add the absolute values: 4 + 6 = 10.
  • Since both original numbers are negative, apply the negative sign to the result.
So, the final answer is -10. This pattern applies whenever you add two negative numbers: sum their absolute values and keep the negative sign!

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Most popular questions from this chapter

Determine the sign of each expression if \(m\) is negative and \(n\) is positive. $$ -\left(\frac{-n}{-m}\right) $$

Simplify. $$ 8(-7)+6(-5) $$

Simplify. $$ 40-3^{2}-2^{3} $$

Divide. $$ -\frac{3}{5} \div\left(-\frac{5}{8}\right) $$

Multiply. \(-2 \cdot(-5) \cdot(-7)\)
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