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Chapter 1: Problem 107

Perform these computations. $$-62+13$$

Short Answer

Expert verified
-49

Step by step solution

01

Identify the numbers

The numbers to compute are -62 and 13.
02

Set up the equation

Write down the equation as -62 + 13.
03

Perform the addition

To add a positive number to a negative number, subtract the smaller number from the larger one and keep the sign of the larger number. So, 62 - 13 = 49. Since 62 is larger and its sign is negative, the result is -49.

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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 can sometimes be tricky, especially when dealing with both positive and negative numbers. The key is to understand the basic rules:
  • If both numbers are positive, simply add them together.
  • If both numbers are negative, add their absolute values and give the result a negative sign.
  • If one number is positive and the other is negative, subtract the smaller absolute value from the larger absolute value. The sign of the result will be the same as the sign of the number with the larger absolute value.

Let's dive deeper into these rules using the given exercise, which requires us to add -62 and 13.
Negative Numbers
Negative numbers can often make math problems seem more difficult than they really are. A negative number is simply a number that is less than zero. These numbers are typically written with a minus sign (-) in front. For example, -62 means 62 units below zero.

When adding a negative number to a positive number (or vice versa), think of it as combining positive and negative quantities. For instance, if you add -62 and 13:
  • Consider -62 as moving 62 units down the number line from zero.
  • Consider 13 as moving 13 units up the number line.
  • The overall movement is 62 units down and 13 units up, so you end up 49 units down from zero.
Step-by-Step Computation
Breaking down math problems step-by-step makes them easier to solve. Here's a detailed look at our example problem, -62 + 13:

  • Step 1: Identify the numbers
    The numbers to compute are -62 and 13.

  • Step 2: Set up the equation
    Write down the equation as -62 + 13.

  • Step 3: Perform the addition
    To add a positive number to a negative number, subtract the smaller number from the larger one and keep the sign of the larger number. So, we compute |62| - |13| = 49. Since 62 is larger and it has a negative sign, our result is -49.

We get that -62 + 13 equals -49. Breaking problems into manageable steps can simplify even the toughest math challenges!

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