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Chapter 4: Problem 3

Find the reciprocal of the given number. $$-17$$

Short Answer

Expert verified
The reciprocal of \(-17\) is \(-\frac{1}{17}\).

Step by step solution

01

Understanding the Problem

To find the reciprocal of a number, we need to understand that the reciprocal is 1 divided by that number. For example, the reciprocal of 5 is \( \frac{1}{5} \). In this case, we are dealing with the number \(-17\).
02

Applying the Formula

Applying the concept of reciprocals, the reciprocal of \( -17 \) is \( \frac{1}{-17} \). This is because the reciprocal of a number \( a \) is \( \frac{1}{a} \).
03

Simplifying the Result

The expression \( \frac{1}{-17} \) can also be written as \(-\frac{1}{17}\). However, both forms represent the same value.

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Key Concepts

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

Reciprocal
The reciprocal of a number is a crucial concept in fractions and mathematics. When we talk about the reciprocal, we mean the value that, when multiplied by the original number, results in 1. For example, the reciprocal of 5 is \( \frac{1}{5} \) because \( 5 \times \frac{1}{5} = 1 \). It's like flipping the number upside-down, swapping the numerator and denominator.
  • To find the reciprocal of a whole number, place 1 over that number.
  • For a fraction, simply flip the numerator and denominator.

When we deal with decimals or mixed numbers, convert them into simple fractions first. Understanding reciprocals helps in dividing fractions because dividing by a fraction is the same as multiplying by its reciprocal.
Negative Numbers
Negative numbers present an interesting twist in mathematics. They are numbers less than zero, depicted with a minus (-) sign. When you work with negative numbers, especially with reciprocals, the principles remain the same, but the negative sign adds a layer.
  • To find the reciprocal of a negative number, retain the negative sign in the reciprocal.
  • A negative divided by a positive results in a negative, hence the reciprocal of \(-17\) is \(-\frac{1}{17}\).

Knowing how to handle negatives is important in solving equations and understanding directional quantities in real-life scenarios like temperature or debt.
Simple Fractions
Simple fractions are the building blocks of more complex mathematical concepts. A simple fraction consists of a numerator (top number) and a denominator (bottom number). For instance, in \( \frac{1}{2} \), 1 is the numerator and 2 is the denominator.
  • Every whole number can be expressed as a fraction with a denominator of 1, e.g., 17 as \( \frac{17}{1} \).
  • Finding reciprocals is particularly straightforward with simple fractions: just swap the positions of numerator and denominator.

Understanding simple fractions is foundational not just for math classes, but for practical tasks such as dividing recipes or understanding ratios. Mastering this concept paves the way for more complex arithmetic operations.

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Most popular questions from this chapter

Solve the equation and simplify your answer. $$-2 x=9 x-4$$

Solve the equation and simplify your answer. $$x-\frac{3}{4}=\frac{1}{4}$$

Solve the equation and simplify your answer. $$-\frac{7}{2} x-\frac{5}{4}=\frac{4}{5}$$

At a local basketball game, announcers informed the crowd that attendance for the game was 5,394 . If this is \(2 / 7\) of the capacity, find the full seating capacity for the basketball stadium.

Solve the equation and simplify your answer. $$-\frac{9}{7} x+\frac{9}{2}=-\frac{5}{2}$$
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