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Chapter 1: Problem 89

Simplify each expression. $$-6.7-(-2.5)$$

Short Answer

Expert verified
\(-4.2\)

Step by step solution

01

Observe the expression

The expression is \(-6.7-(-2.5)\). In this expression, we see that we are subtracting a negative number. This essentially means that we add its absolute value.
02

Transforming the expression

Knowing from the previous step that subtracting a negative is akin to addition, we can rewrite the expression as: \(-6.7 + 2.5\).
03

Perform the addition

Finally, we perform the addition, which results in: \(-4.2\).

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Key Concepts

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

Subtracting Negative Numbers
When you encounter a negative sign in front of a negative number, it might seem a bit tricky, but it's actually quite straightforward. Subtracting a negative number is like flipping the switch from subtracting to adding. This is because the negative sign in front of the negative number effectively "cancels out," much like how subtracting goes in the opposite direction of adding. Here's how it works:
  • The expression \(-6.7-(-2.5)\) implies that you have negative 6.7, and you are subtracting negative 2.5 from it.
  • Subtracting \(-2.5\) is akin to an addition operation. So we effectively transform this operation into \(-6.7 + 2.5\).
With this knowledge, navigating through expressions that involve subtracting negative numbers becomes much easier. It's all about changing the subtraction to an addition.
Absolute Value
The absolute value of a number refers to its distance from zero on the number line, without considering its direction. It's always a non-negative number. The importance of understanding absolute values is that they help us convert complex expressions into more easily manageable ones.
  • For instance, \(-2.5\) has an absolute value of \(2.5\) because it's 2.5 units away from zero.
  • The absolute value disregards whether the number is positive or negative, focusing only on magnitude.
When working with subtraction of negative numbers or even in other operations, knowing the absolute value allows you to simplify expressions and transform problems into more friendly forms.
Addition of Decimals
Adding decimals is much like regular addition, but it requires you to align the decimal points to ensure accuracy. This precision is what helps in obtaining an accurate result.
  • To add \(-6.7 + 2.5\), align these numbers by their decimal points:
  • \(-6.7\) and \(2.5\), paying special attention that digits line up properly.
  • You perform addition from right to left as you would in any other arithmetic operation, accounting carefully for any changes in sign.
Adding decimals correctly is crucial, especially in real-world contexts where precision can make a significant difference.

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Most popular questions from this chapter

Consider the following sets: the integers, natural numbers, even and odd integers, positive and negative numbers, prime and composite numbers, and rational numbers. Find a number that fits in as many of these categories as possible.

Use the distributive property to write each expression without parentheses. $$-a(a+b)$$

Explain why there is no greatest natural number.

A girl had \(d\) dollars, and her brother had \(\$ 5\) more than three times that amount. How much did the brother have?

Which property of real numbers justifies each statement? $$3+(-3)=0$$
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