2.2 The real number line and the real numbers  (Page 2/2)

Is every natural number a whole number?

Is every whole number an integer?

Is every integer a rational number?

Is every rational number a real number?

Is every integer a natural number?

Is there an integer that is a natural number?

Are all positive numbers greater than 0?

Are all positive numbers greater than all negative numbers?

Is 0 greater than all negative numbers?

Is there a largest positive number? Is there a smallest negative number?

How many real numbers are there? How many real numbers are there between 0 and 1?

What whole numbers can replace $x$ so that the following statement is true?

$-3\le x<3$

Draw a number line that extends from $-5$ to 3 and place points at all numbers greater than or equal to $-4$ but strictly less than 2.

$\frac{1}{2}$

$-12$

0

$-24\frac{7}{8}$

$86.3333\dots$

$49.125125125\dots$

$-15.07$

$1\frac{1}{2}$

$-2$

$-\frac{1}{8}$

Is 0 a positive number, negative number, neither, or both?

An integer is an even integer if it can be divided by 2 without a remainder; otherwise the number is odd. Draw a number line that extends from $-5$ to 5 and place points at all negative even integers and at all positive odd integers.

Draw a number line that extends from $-5$ to 5. Place points at all integers strictly greater than $-3$ but strictly less than 4.

$-5$ and $-2$

$-3$ and 4

$-4$ and 0

Draw a number line that extends from $-5$ to 5. Is it possible to locate any numbers that are strictly greater than 3 but also strictly less than $-2$ ?

$-5\ast -1$

$-3\ast 0$

$-4\ast 7$

$6\ast -1$

$-\frac{1}{4}\ast -\frac{3}{4}$

Is there a largest real number? If so, what is it?

Is there a largest integer? If so, what is it?

Is there a largest two-digit integer? If so, what is it?

Is there a smallest integer? If so, what is it?

Is there a smallest whole number? If so, what is it?

$\begin{array}{cc}-1\le x\le 5& x\text{an}\text{integer}\end{array}$

$\begin{array}{cc}-7<x<-1,& x\text{an}\text{integer}\end{array}$

$\begin{array}{cc}-3\le x\le 2,& x\text{a}\text{natural}\text{number}\end{array}$

$\begin{array}{cc}-15<x\le -1,& x\text{a}\text{natural}\text{number}\end{array}$

$\begin{array}{cc}-5\le x<5,& x\text{a}\text{whole}\text{number}\end{array}$

The temperature in the desert today was ninety-five degrees. Represent this temperature by a rational number.

The temperature today in Colorado Springs was eight degrees below zero. Represent this temperature with a real number.

Is every integer a rational number?

Is every rational number an integer?

Can two rational numbers be added together to yield an integer? If so, give an example.

0 and 2?

$-5$ and 0?

0 and 6?

$-8$ and 0?

$-3$ and 4?

$m$ and $n$ , $m>n$ ?

$-a$ and $-b$ , $-b>-a$ ?

( [link] ) Find the value of $6+3(15-8)-4$ .

( [link] ) Find the value of $5(8-6)+3(5+2\cdot 3)$ .

( [link] ) Are the statements $y<4$ and $y\ge 4$ the same or different?

( [link] ) Use algebraic notation to write the statement "six times a number is less than or equal to eleven."

( [link] ) Is the statement $8(15-3\cdot 4)-3\cdot 7\ge 3$ true or false?