Problem 31 Subtract. $$ -42-26 $$... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 10: Problem 31

Subtract. $$ -42-26 $$

Short Answer

Expert verified

The result is \ -68 \.

Step by step solution

Understand the Problem

The expression to solve is $-42 - 26$. The goal is to subtract 26 from -42.

Rewrite the Expression

Subtraction of a number is the same as adding its negative. So, rewrite $-42 - 26$ as $-42 + (-26)$.

Add the Negative Numbers

Add $-42$ and $-26$ together. When adding two negative numbers, the result is also negative, and the magnitude is the sum of the magnitudes of the numbers: \|-42| + |-26| = 42 + 26 = 68.

Combine the Results

Since both numbers are negative, the final result is negative: $-42) + (-26) = -68$.

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Key Concepts

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

subtracting negative numbers

When it comes to subtracting negative numbers, you can think about it in a unique way. Instead of subtracting, you actually add the opposite. This might sound confusing, but it's straightforward.
Instead of doing $-42 - 26$, rewrite it as $-42 + (-26)$. Notice how subtraction becomes addition. In other words, subtracting a number is the same as adding its negative.
To make things clear, if you have a number line, move to the left because you are adding a negative number, which decreases the value further.

absolute values

Absolute values represent the distance of a number from zero, regardless of direction. This means that whether a number is positive or negative, its absolute value is positive.
For example, the absolute value of $-42$ is 42, and the absolute value of $-26$ is 26. These absolute values help when adding or subtracting negative numbers.
To clarify: \| -42 | = 42\ and \| -26 | = 26\.
This concept becomes important because when you translate subtraction into adding a negative, you focus on these absolute values to find your total distance from zero.

adding negative numbers

Adding negative numbers involves a few straightforward steps. When you add two negative numbers, imagine you are combining their distances from zero, but in the opposite direction on the number line.
For instance, with -42 and -26, rewrite this as $-42 + (-26)$.
You simply add their absolute values: \42 + 26 = 68\. Then, because both numbers were negative, your result remains negative: \ -68.\
In summary:

Identify the numbers' absolute values.
Add these absolute values together.
Since both numbers were negative, apply the negative sign to the result.

So, \-42 + (-26) = -68\.

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91影视

Subtract. $$ -42-26 $$

Short Answer

Step by step solution

Understand the Problem

Rewrite the Expression

Add the Negative Numbers

Combine the Results

Key Concepts

subtracting negative numbers

absolute values

adding negative numbers

One App. One Place for Learning.

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