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Chapter 0: Problem 148

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Every rational number is an integer.

Short Answer

Expert verified
The statement 'Every rational number is an integer' is false. A correct version of the statement is 'Every integer is a rational number'.

Step by step solution

01

Understanding the definitions

A rational number is any number that can be expressed as the fraction of two integers and an integer is a whole number, either positive, negative or zero.
02

Examine the statement

The statement says 'Every rational number is an integer'. This means every number that can be expressed as a fraction of two integers is a whole number.
03

Evaluate the statement

Consider the rational number 1/2, it's a fraction and cannot be represented as a whole number, contradicting our statement. Thus the statement is false.
04

Correct the Statement

A more accurate statement would be 'Every integer is a rational number'. This is because any integer \(n\) can be expressed as the ratio of \(n/1\), which fits the definition of a rational number.

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Most popular questions from this chapter

If you are given a quadratic equation, how do you determine which method to use to solve it?

This will help you prepare for the material covered in the next section. Multiply and simplify: \(12\left(\frac{x+2}{4}-\frac{x-1}{3}\right)\).

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. An elevator at a construction site has a maximum capacity of 3000 pounds. If the elevator operator weighs 245 pounds and each cement bag weighs 95 pounds, how many bags of cement can be safely lifted on the elevator in one trip?

In Exercises \(133-136\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$7^{\frac{1}{2}} \cdot 7^{\frac{1}{2}}=49$$

Find \(b\) such that \(\frac{7 x+4}{b}+13=x\) will have a solution set given by \(\\{-6\\}\).
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