# 1.8 The real numbers  (Page 5/13)

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$\begin{array}{ccccccc}\hfill \frac{7}{4}=1\frac{3}{4}\hfill & & & \hfill -\phantom{\rule{0.2em}{0ex}}\frac{9}{2}=-4\frac{1}{2}\hfill & & & \hfill \frac{8}{3}=2\frac{2}{3}\hfill \end{array}$

[link] shows the number line with all the points plotted.

Locate and label the following on a number line: $4,\frac{3}{4},-\phantom{\rule{0.2em}{0ex}}\frac{1}{4},-3,\frac{6}{5},-\phantom{\rule{0.2em}{0ex}}\frac{5}{2},\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}\frac{7}{3}.$

Locate and plot the integers, $4,-3.$

Locate the proper fraction $\frac{3}{4}$ first. The fraction $\frac{3}{4}$ is between 0 and 1. Divide the distance between 0 and 1 into four equal parts then, we plot $\frac{3}{4}.$ Similarly plot $-\phantom{\rule{0.2em}{0ex}}\frac{1}{4}.$

Now locate the improper fractions $\frac{6}{5},-\phantom{\rule{0.2em}{0ex}}\frac{5}{2},\frac{7}{3}.$ It is easier to plot them if we convert them to mixed numbers and then plot them as described above: $\frac{6}{5}=1\frac{1}{5},-\phantom{\rule{0.2em}{0ex}}\frac{5}{2}=-2\frac{1}{2},\frac{7}{3}=2\frac{1}{3}.$

Locate and label the following on a number line: $-1,\frac{1}{3},\frac{6}{5},-\phantom{\rule{0.2em}{0ex}}\frac{7}{4},\frac{9}{2},5,-\phantom{\rule{0.2em}{0ex}}\frac{8}{3}.$

Locate and label the following on a number line: $-2,\frac{2}{3},\frac{7}{5},-\phantom{\rule{0.2em}{0ex}}\frac{7}{4},\frac{7}{2},3,-\phantom{\rule{0.2em}{0ex}}\frac{7}{3}.$

In [link] , we’ll use the inequality symbols to order fractions. In previous chapters we used the number line to order numbers.

• a<b a is less than b ” when a is to the left of b on the number line
• a>b a is greater than b ” when a is to the right of b on the number line

As we move from left to right on a number line, the values increase.

Order each of the following pairs of numbers, using<or>. It may be helpful to refer [link] .

$-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}___-1$ $-3\frac{1}{2}___-3$ $-\phantom{\rule{0.2em}{0ex}}\frac{3}{4}___-\phantom{\rule{0.2em}{0ex}}\frac{1}{4}$ $-2___-\phantom{\rule{0.2em}{0ex}}\frac{8}{3}$

Be careful when ordering negative numbers.

1. $\begin{array}{cccccc}& & & & & -\phantom{\rule{0.2em}{0ex}}\frac{2}{3}___-1\hfill \\ -\phantom{\rule{0.2em}{0ex}}\frac{2}{3}\phantom{\rule{0.2em}{0ex}}\text{is to the right of}\phantom{\rule{0.2em}{0ex}}-1\phantom{\rule{0.2em}{0ex}}\text{on the number line.}\hfill & & & & & -\phantom{\rule{0.2em}{0ex}}\frac{2}{3}>-1\hfill \end{array}$

2. $\begin{array}{cccccc}& & & & & -3\frac{1}{2}___-3\hfill \\ -3\frac{1}{2}\phantom{\rule{0.2em}{0ex}}\text{is to the left of}\phantom{\rule{0.2em}{0ex}}-3\phantom{\rule{0.2em}{0ex}}\text{on the number line.}\hfill & & & & & -3\frac{1}{2}<-3\hfill \end{array}$

3. $\begin{array}{cccccc}& & & & & -\phantom{\rule{0.2em}{0ex}}\frac{3}{4}___-\phantom{\rule{0.2em}{0ex}}\frac{1}{4}\hfill \\ -\phantom{\rule{0.2em}{0ex}}\frac{3}{4}\phantom{\rule{0.2em}{0ex}}\text{is to the left of}\phantom{\rule{0.2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\frac{1}{4}\phantom{\rule{0.2em}{0ex}}\text{on the number line.}\hfill & & & & & -\phantom{\rule{0.2em}{0ex}}\frac{3}{4}<-\phantom{\rule{0.2em}{0ex}}\frac{1}{4}\hfill \end{array}$

4. $\begin{array}{cccccc}& & & & & -2___-\phantom{\rule{0.2em}{0ex}}\frac{8}{3}\hfill \\ -2\phantom{\rule{0.2em}{0ex}}\text{is to the right of}\phantom{\rule{0.2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\frac{8}{3}\phantom{\rule{0.2em}{0ex}}\text{on the number line.}\hfill & & & & & -2>-\phantom{\rule{0.2em}{0ex}}\frac{8}{3}\hfill \end{array}$

Order each of the following pairs of numbers, using<or>:

$-\phantom{\rule{0.2em}{0ex}}\frac{1}{3}___-1$ $-1\frac{1}{2}___-2$ $-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}___-\phantom{\rule{0.2em}{0ex}}\frac{1}{3}$ $-3___-\phantom{\rule{0.2em}{0ex}}\frac{7}{3}.$

> > < <

Order each of the following pairs of numbers, using<or>:

$-1___-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}$ $-2\frac{1}{4}___-2$ $-\phantom{\rule{0.2em}{0ex}}\frac{3}{5}___-\phantom{\rule{0.2em}{0ex}}\frac{4}{5}$ $-4___-\phantom{\rule{0.2em}{0ex}}\frac{10}{3}.$

< < > <

## Locate decimals on the number line

Since decimals are forms of fractions, locating decimals on the number line is similar to locating fractions on the number line.

Locate 0.4 on the number line.

A proper fraction has value less than one. The decimal number 0.4 is equivalent to $\frac{4}{10},$ a proper fraction, so 0.4 is located between 0 and 1. On a number line, divide the interval between 0 and 1 into 10 equal parts. Now label the parts 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0. We write 0 as 0.0 and 1 and 1.0, so that the numbers are consistently in tenths. Finally, mark 0.4 on the number line. See [link] .

Locate on the number line: 0.6.

Locate on the number line: 0.9.

Locate $-0.74$ on the number line.

The decimal $-0.74$ is equivalent to $-\phantom{\rule{0.2em}{0ex}}\frac{74}{100},$ so it is located between 0 and $-1.$ On a number line, mark off and label the hundredths in the interval between 0 and $-1.$ See [link] .

Locate on the number line: $-0.6.$

Locate on the number line: $-0.7.$

Which is larger, 0.04 or 0.40? If you think of this as money, you know that $0.40 (forty cents) is greater than$0.04 (four cents). So,

$0.40>0.04$

Again, we can use the number line to order numbers.

• a<b a is less than b ” when a is to the left of b on the number line
• a>b a is greater than b ” when a is to the right of b on the number line

Where are 0.04 and 0.40 located on the number line? See [link] .

We see that 0.40 is to the right of 0.04 on the number line. This is another way to demonstrate that 0.40>0.04.

How does 0.31 compare to 0.308? This doesn’t translate into money to make it easy to compare. But if we convert 0.31 and 0.308 into fractions, we can tell which is larger.

#### Questions & Answers

I don't see where the answers are.
Ed
Cindy and Richard leave their dorm in Charleston at the same time. Cindy rides her bicycle north at a speed of 18 miles per hour. Richard rides his bicycle south at a speed of 14 miles per hour. How long will it take them to be 96 miles apart?
3
Christopher
18t+14t=96 32t=96 32/96 3
Christopher
show that a^n-b^2n is divisible by a-b
What does 3 times your weight right now
Use algebra to combine 39×5 and the half sum of travel of 59+30
Cherokee
What is the segment of 13? Explain
Cherokee
my weight is 49. So 3 times is 147
Cherokee
kg to lbs you goin to convert 2.2 or one if the same unit your going to time your body weight by 3. example if my body weight is 210lb. what would be my weight if I was 3 times as much in kg. that's you do 210 x3 = 630lb. then 630 x 2.2= .... hope this helps
tyler
How to convert grams to pounds?
paul
What is the lcm of 340
Yes
Cherokee
How many numbers each equal to y must be taken to make 15xy
15x
Martin
15x
Asamoah
15x
Hugo
1y
Tom
1y x 15y
Tom
find the equation whose roots are 1 and 2
(x - 2)(x -1)=0 so equation is x^2-x+2=0
Ranu
I believe it's x^2-3x+2
NerdNamedGerg
because the X's multiply by the -2 and the -1 and than combine like terms
NerdNamedGerg
find the equation whose roots are -1 and 4
Ans = ×^2-3×+2
Gee
find the equation whose roots are -2 and -1
(×+1)(×-4) = x^2-3×-4
Gee
Quadratic equations involving factorization
there's a chatting option in the app wow
Nana
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Nana
Nice to meet you all
Nana
you too.
Joan
😃
Nana
Hey you all there are several Free Apps that can really help you to better solve type Equations.
Debra
Debra, which apps specifically. ..?
Nana
am having a course in elementary algebra ,any recommendations ?
samuel
Samuel Addai, me too at ucc elementary algebra as part of my core subjects in science
Nana
me too as part of my core subjects in R M E
Ken
at ABETIFI COLLEGE OF EDUCATION
Ken
ok great. Good to know.
Joan
5x + 1/3= 2x + 1/2
sanam
Plz solve this
sanam
5x - 3x = 1/2 - 1/3 2x = 1/6 x = 1/12
Ranu
Thks ranu
sanam
a trader gains 20 rupees loses 42 rupees and then gains ten rupees Express algebraically the result of his transactions
a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions
vinaya
a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions
vinaya
a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions
vinaya
Kim is making eight gallons of punch from fruit juice and soda. The fruit juice costs $6.04 per gallon and the soda costs$4.28 per gallon. How much fruit juice and how much soda should she use so that the punch costs $5.71 per gallon? Mohamed Reply (a+b)(p+q+r)(b+c)(p+q+r)(c+a) (p+q+r) muhammad Reply 4x-7y=8 2x-7y=1 what is the answer? Ramil Reply x=7/2 & y=6/7 Pbp x=7/2 & y=6/7 use Elimination Debra true bismark factoriz e usman 4x-7y=8 X=7/4y+2 and 2x-7y=1 x=7/2y+1/2 Peggie Ok cool answer peggie Frank thanks Ramil copy and complete the table. x. 5. 8. 12. then 9x-5. to the 2nd power+4. then 2xto the second power +3x Sandra Reply What is c+4=8 Penny Reply 2 Letha 4 Lolita 4 Rich 4 thinking C+4=8 -4 -4 C =4 thinking I need to study Letha 4+4=8 William During two years in college, a student earned$9,500. The second year, she earned \$500 more than twice the amount she earned the first year.
9500=500+2x
Debra
9500-500=9000 9000÷2×=4500 X=4500
Debra
X + Y = 9500....... & Y = 500 + 2X so.... X + 500 + 2X = 9500, them X = 3000 & Y = 6500
Pbp