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Chapter 1: Problem 52

Subtract. $$ -40-(-40) $$

Short Answer

Expert verified
$$-40 - (-40) = 0$$

Step by step solution

01

- Understand the given expression

The problem is to subtract ewline oindent\text{$$ -40 -(-40) $$}.
02

- Apply the rule on subtracting negative numbers

When subtracting a negative number, the two negative signs become a positive sign: $$ a - (-b) = a + b $$. Therefore, one can rewrite the expression as ewline oindent\text{$$ -40 - (-40)$$ }.
03

- Simplify the expression

Change the subtraction of the negative number to an addition and simplify: $$ -40 - (-40) = -40 + 40.$$.
04

- Perform the addition

Add the numbers: ewlineoindent\text{$$ -40 + 40 = 0 $$}. Therefore, the expression simplifies to 0.

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Key Concepts

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

Negative Numbers
Negative numbers might seem tricky at first, but they follow simple rules and are incredibly useful.
Negative numbers are found below zero on a number line and represent values less than zero.
They are typically used to indicate a loss, decrease, or something in the reverse direction.
For instance, if the temperature drops 10 degrees below zero, it can be represented as -10.
It's crucial to understand the concept of negative numbers to solve various math problems effectively.
Subtraction
Subtraction is one of the four basic arithmetic operations.
It represents the operation of removing objects from a collection.
When we subtract a positive number from another positive number, it means we are taking away that amount.
For example, if you have 5 apples and give away 3, you have 2 apples left. This can be written as 5 - 3 = 2.
But what happens when we subtract negative numbers? Subtracting a negative number involves an extra step, which can be confusing at first.
This is where the rule of double negatives comes into play.
Addition
Addition is another fundamental arithmetic operation, vital for daily calculations.
Adding means finding the total or sum by combining two or more numbers.
When dealing with subtracting negative numbers, the operation can often be converted to addition.
For example, subtracting a negative number becomes adding its positive counterpart.
This is because two negative signs cancel each other out, converting the subtraction into an addition.
For instance, in the exercise `-40 - (-40)`, the subtraction of a negative 40 turns into adding 40, simplifying the problem to -40 + 40.
Thus, the solution simplifies to 0, effectively explaining the role of addition in such problems.

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