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Chapter 1: Problem 42

Find (a) the opposite (or additive inverse) of each number and (b) the absolute value of each number. $$ -\frac{2}{5} $$

Short Answer

Expert verified
Opposite: \( \frac{2}{5} \), Absolute value: \( \frac{2}{5} \).

Step by step solution

01

Identify the given number

The number given is \( -\frac{2}{5} \).
02

Find the opposite (additive inverse)

To find the opposite of a number, change its sign. The opposite of \( -\frac{2}{5} \) is \( \frac{2}{5} \).
03

Find the absolute value

The absolute value of a number is always positive and represents the distance of the number from zero on the number line. The absolute value of \( -\frac{2}{5} \) is \( \frac{2}{5} \).

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Key Concepts

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

opposite of a number
Understanding the opposite of a number is a fundamental math concept. The opposite of a number, also known as the additive inverse, changes the sign of the number. If you have a positive number, its opposite will be negative, and vice versa. For example, the opposite of \( 3 \) is \( -3 \). Similarly, the opposite of a negative fraction, like \( -\frac{2}{5} \), is \( \frac{2}{5} \). This means we simply change the sign from negative to positive.
absolute value
Absolute value is a concept that tells us how far a number is from zero on the number line, regardless of direction. The absolute value of any number is always non-negative. This is because distance can never be negative. To find the absolute value, we ignore the sign of the number. For instance, the absolute value of \( -\frac{2}{5} \) is \( \frac{2}{5} \), because distance is always positive. You can think of it as stripping away the sign and just looking at the 'size' of the number.
negative fractions
Negative fractions can seem confusing at first, but they're just like negative whole numbers. A fraction like \( -\frac{2}{5} \) means that we're dealing with a quantity that is less than zero. To handle negative fractions:
  • Identify the negative sign and understand it means the value is less than zero.
  • Perform operations on the fraction just like you would with positive fractions.
  • Pay attention to the sign during addition, subtraction, multiplication, and division.
Understanding these fractions helps in finding their opposites and absolute values, as seen in our examples.

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Most popular questions from this chapter

Write a numerical expression for each phrase and simplify. 1.85 more than the sum of \(-1.25\) and \(-4.75\)

Find each difference. $$ 2-(3-5) $$

Decide whether each statement is true or false. \(-|-5| \geq-|-9|\)

A manufacturer has fixed costs of \(\$ 1000\) to produce widgets. Each widget costs \(\$ 5\) to make. The fixed cost to produce gadgets is \(\$ 750,\) and each gadget costs \(\$ 3\) to make. Write an expression for the cost to make \(x\) widgets. (Hint: The cost will be the sum of the fixed cost and the cost per item times the number of items.)

Perform each indicated operation. $$ 6+(-9-2) $$
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